Learning Platforms

• Derivative Calculus Solver — A step-by-step differentiation tool focusing on the chain rule and substitution logic.

Books

• The Math Behind Artificial Intelligence - Tiago Capelo Monteiro (freeCodeCamp)

Tools

• Structural Engineering Tools (SEPCO Engineering) (⭐0) - Free online calculators for beam diagrams, Canadian steel section properties, and pressure conversions.

Tools

• RunMat (⭐188) - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution.

Tools

• MathFlow (⭐50) - C# math expression library with symbolic computation (differentiation, simplification, equation solving)

Books

• Math for Frontend Web Dev

• Grokking Statistics

Combinatorics / Lie Algebras

• 📝 Basic Combinatorics - Carl G. Wagner (University of Tennessee)

Combinatorics / Graph Theory

• 📝 Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform - Hadjoudj Mohammed Islam

Analysis / Chaos Theory

• 📝 Chaos: Making a New Science - James Gleick

• 📝 Complexity: A Guided Tour - Melanie Mitchell (Oxford University)

Number Theory / Algebraic Number Theory

• 📝 Introduction to Algebraic Number Theory - F. Oggier

Algebra / Abstract Algebra

• 📝 Algebraic Methods - F. Oggier

Tools

• Corca Editor

Algebra / Linear Algebra

• 📖 Linear Algebra Done Right - Sheldon Axler

Foundations of Mathematics / Transition To Pure Rigour Math

• 📝 Book of Proof - Richard Hammak (Virginia Commonwealth University)

Geometry and Topology / Differential Geometry

• 📝 Notes on Differential Geometry and Lie Groups - Jean Gallier (University of Pennsylvania)

Youtube Series

• The Math Sorcerer

Learning Platforms

• Math Academy

Tools

• Midpoint Calculator

• Quartiles Calculator

Meetings and Conferences

• MathsJam - monthly local recreational maths/puzzle meetups and an annual gathering in Staffordshire, England

• Talking Maths in Public - a conference for maths communicators, running every two years, usually in the UK

• Bridges - an annual conference on mathematical connections in art, music, architecture, and culture. The 2025 meeting is in Eindhoven, Netherlands.

Foundations of Mathematics / Transition To Pure Rigour Math

• 📖 How to Prove It: A Structured Approach (3rd Edition) - Daniel J. Velleman (Professor).

Tools

• Mathcheap

Algebra / Galois Theory

• 📝 Galois Theory - Ian Stewart

• 📝 Galois Theory — Tom Leinster (University of Edinburgh)

Tools

• Finance calculators

Numerical Analysis / Stochastic processes

• 📝🎥 Advanced Linear Algebra: Foundations to Frontiers - Robert van de Geijn, Margaret Myers (University of Texas at Austin)

Encyclopedia

• 💲 The Princeton Companion to Mathematics - Timothy Gowers (Professor, Fields medallist), June Barrow-Green (Professor), and Imre Leader (Professor).

• 💲 Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.

Analysis / Functional Analysis

• 📝 An Introduction to Functional Analysis - Laurent W. Marcoux (University of Waterloo)

• 📝 Functional Analysis Lecture Notes - T.B. Ward (University of East Anglia)

Numerical Analysis / Stochastic processes

• 📝 Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods - Alfred Schmidt, Arsen Narimanyan

Numerical Analysis / Stochastic processes

• 📝 Lectures In Basic Computational Numerical Analysis - J. M. McDonough (University of Kentucky)

Number Theory / Surreal Numbers

• 📝 Yet Another Introductory Number Theory Textbook - Jonathan A. Poritz

Geometry and Topology / Algebraic Statistics

• 📝 Lectures on Algebraic Statistics - Mathias Drton, Bernd Sturmfels, Seth Sullivant

• 📝 An Introduction to Algebraic Statistics - Cristiano Bocci, Luca Chiantini and Anthony V. Geramita

• 📝 Algebraic Statistics - Karl-Heinz Zimmermann

• 📝 Algebraic Statistics for Computational Biology - Pachter, and Sturmfels.

Encyclopedia

• The On-Line Encyclopedia of Integer Sequences - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane.

Youtube Series

• StatQuest

Youtube Series

• Brandon Foltz

• 3Blue1Brown

• NPTEL

• PatrickJMT

• Professor Leonard
  • Precalculus - College Algebra/Trigonometry
  • Calculus 1
  • Calculus 2
  • Calculus 3
  • Differential Equations
  • To The Point Math

• Crash Course

• Harvard

• MIT OpenCourseWare

• Mathologer

• The Math District

• Mathematical Monk

Tools

• CopyPasteMathjax

Analysis / Measure Theory

• 📝 An Introduction to Measure Theory - Terence Tao (UCLA)

Numerical Analysis / Stochastic processes

• 📝 Introduction to Numerical Analysis - Doron Levy (University of Maryland)

• 📝 Numerical Analysis for Engineers - Douglas Wilhelm Harder

Learning Platforms

• Oxford Mathematics

Mathematical Physics / Stochastic processes

• Theoretical Computer Science (⭐1.1k)

Magazines

• Quanta Magazine - Features latest research breakthroughs in an accessible style for non-experts.

• Bulletin of the American Mathematical Society - Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic.

• Notices of the American Mathematical Society - Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research.

• European Mathematical Society Magazine - The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items.

• Mathematics Today by Institute of Mathematics and its Applications - News, opinions, and articles related to mathematics, so the reader stays updated.

• Crux Mathematicorum by Canadian Mathematical Society - source of unique and challenging mathematical problems designed for the secondary and undergraduate levels. It includes an Olympiad Corner which is helpful for math competitions.

Learning Platforms

• Almost Fun

Misc

• Fabrice Baudoin's Notes - Both research and lecture notes on many topics, Including Diffusions on foliated manifold, Stochastic Calculus, Global analysis in Dirichlet spaces, and more.

Foundations of Mathematics / Logic

• 📝 Computability - An introduction to recursive function theory - Nigel Cutland (University of Hull)

Tools

• xhub

Tools

• Unit Converter

Books

• Free Mathematics Books (⭐383k)

Geometry and Topology / Algebraic Geometry

• 📝 A Brief Introduction to Algebraic Geometry - R.C. Churchill

Learning Platforms

• Ximera : free interactive mathematics textbooks (Ohio State University)

Geometry and Topology / Differential Geometry

• 📝 Discrete Differential Geometry - Keenan Crane

Analysis / Complex Analysis

• 📝 A Concise Course in Complex Analysis and Riemann Surfaces - Wilhelm Schlag

Tools

• Maxima

Tools

• Free Math

Learning Platforms

• Calculus.org

Foundations of Mathematics / Logic

• 📝 Introduction to Logic - Michael Genesereth, Eric Kao (Stanford University)

Number Theory / Surreal Numbers

• 📝 Elementary Number Theory - W. Edwin Clark (University of South Florida)

• 📝 Number Theory: A Contemporary Introduction - Pete L. Clark

Geometry and Topology / Topology

• 📝 Topology Topics

Analysis / Complex Analysis

• 📝 Introduction to Complex Analysis - Michael Taylor

Mathematical Physics / Stochastic processes

• Evan Chen - MIT. 2012 ~ 2018. Covers Combinatorics, Number Theory, Honors Algebra, Set Theory, Real Analysis, Graph Theory, and more.

• Dexter Chua - Harvard. 2013 ~ 2018. Covers Analysis, Probability, Linear Algebra, Complex Analysis, Numerical Analysis, Statistics, Optimization, Algebraic Topology, Quantum Field Theory, and more.

Algebra / Analytic Number Theory

• 📝 Understanding Algebra - James W. Brennan

Analysis / Real Analysis

• 📝 Precalculus - Carl Stitz, Jeff Zeager

Analysis / Harmonic Analysis

• 📝 Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications - Julius O. Smith III (Stanford University)

Tools

• GeoGebra

• Macaulay2

• Singular

• GNU Octave

• Magma

• Maple

• Matlab

• Wolfram Mathematica

Foundations of Mathematics / Type Theory

• 📝 Programming in Martin-Lof’s Type Theory - Bengt Nordstrom, Kent Petersson, Jan M. Smith

Foundations of Mathematics / Logic

• 📝 Open Logic Textbook - collaborative effort, main contributors listed here

Foundations of Mathematics / Category Theory

• 📝 Category Theory in Context - Emily Riehl (John Hopkins University)

Foundations of Mathematics / Logic

• 📝 QED - an interactive textbook - Terence Tao

Misc

• Recreations in Math - H. E. Licks (1917)

• Magic Squares and Cubes - W. S. Andrews (1917)

Algebra / Analytic Number Theory

• 📝 First Course in Algebra - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1910)

• 📝 Second Course in Algebra - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1911)

• 📝 Algebra: An Elementary Text-Book, Part I - G. Chrystal (1904)

• 📝 Algebra: An Elementary Text-Book, Part II - G. Chrystal (1900)

Geometry and Topology / Graph Theory

• 📝 Plane Geometry - George Wentworth and David Eugene Smith (1913)

• 📝 Planes and Spherical Trigonometry - George Wentworth and David Eugene Smith (1915)

• 📝 Coordinate Geometry - Henry Buchard Fine and Henry Dallas Thompson (1911)

• 📝 Analytic Geometry - Lewis Parker Siceloff, George Wentworth, David Eugene Smith (1922)

Analysis / Real Analysis

• 📝 Calculus Made Easy - Silvanus P. Thompson (1910)

• 📝 Elements of Differential and Integral Calculus - William Anthony Granville (1911)

Analysis / Ordinary Differential Equations

• 📝 Differential Equations - H. B. Phillips (1922)

Learning Platforms

• Mathigon

Misc

• Convex Optimization - Stephen Boyd and Lieven Vandenberghe

Foundations of Mathematics / Logic

• 📝 Logic and Proof - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn

Algebra / Linear Algebra

• 📝 Interactive Linear Algebra - Dan Margalit and Joseph Rabinoff

• 📝 Linear Algebra, Infinite Dimensions, and Maple - James Herod

Geometry and Topology / Graph Theory

• 📝 Byrne's Euclid - Oliver Byrne

Analysis / Complex Analysis

• 📝 Complex Analysis - Juan Carlos Ponce Campuzano

Probability and Statistics / Probability Theory

• 📝 Foundations of Constructive Probability Theory - Yuen-Kwok Chan

Probability and Statistics / Statistics

• 📝 Statistical Thinking for the 21st Century - Russell A. Poldrack

• 📝 Odds and Ends: Introducing Probability & Decision with a Visual Emphasis - Jonathan Weisberg

• 📝 Seeing Theory - Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang

• 📝 Statistics Done Wrong - Alex Reinhart

• 📝 All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman

Mathematics for Computer Science / Stochastic processes

• 📝 The Chaos Textbook: Mathematics in the age of the computer - Glenn Elert

Blogs

• MathematicsIsAScience - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA)

Signal processing / Stochastic processes

• 📝 Think DSP - Allen B. Downey

Foundations of Mathematics / Type Theory

• 📝 Type Theory and Functional Programming - Simon Thompson

Foundations of Mathematics / Type Theory

• 📝 Proofs and Types - Jean-Yves Girard

• 📝 Intuitionistic Type Theory - Per Martin-Lof

Algebra / Linear Algebra

• 📝 Immersive Linear Algebra - J. Ström, K. Åström, and T. Akenine-Möller

Tools

• Sympy

• Sagemath

Algebra / Abstract Algebra

• 📝 Introduction to Abstract Algebra - D. S. Malik, John N. Mordeson, M.K. Sen (Creighton University)

Foundations of Mathematics / Category Theory

• 📝 Category Theory for Computing Science - Michael Barr, Charles Wells

Algebra / Abstract Algebra

• 📝 Abstract Algebra: Harvard Extension (Archived) - Benedict Gross

• 📝 Abstract Algebra: Harvard Extension Videos - Benedict Gross

Algebra / Linear Algebra

• 📝 Linear Algebra Done Wrong - Sergei Treil

Analysis / Real Analysis

• 📝 Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis" - George M. Bergman

Analysis / Functional Analysis

• 📝 Theory of Functions of a Real Variable - Shlomo Sternberg

Learning Platforms

• Brilliant

• WooTube

Blogs

• Mathsisfun simple text lightweight site for students up to highschool

Geometry and Topology / Topology

• 📝 Elementary Applied Topology - Robert Ghrist (UPenn)

Geometry and Topology / Algebraic Geometry

• 📝 The Stacks Project - Maintained by Aise Johan de Jong (Columbia)

Foundations of Mathematics / Category Theory

• 📝 Abstract and Concrete Categories: The Joy of Cats - Jiri Adamek, Horst Herrlich, George Strecker

• 📝 Seven Sketches in Compositionality: An Invitation to Applied Category Theory - Brendan Fong and David I. Spivak (MIT)

Tools

• Symbolab

• Desmos

• Math Words

• Wolfram Alpha

Algebra / Linear Algebra

• 📝 Introduction to Applied Linear Algebra - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA)

Misc

• Topology Atlas

Probability and Statistics / Stochastic processes

• 📝 Convergence of Stochastic Processes - David Pollard

Foundations of Mathematics / Set Theory

• 📝 Sets, Relations, Functions - Ivo Düntsch, Günther Gediga

Foundations of Mathematics / Logic

• 📝 Predictive Arithmetic - Edward Nelson

• 📝 Proofs and Concepts: the fundamentals of abstract mathematics - Joy Morris, Dave Morris

• 📝 Mathematical Reasoning: Writing and Proof - Ted Sundstrom

Foundations of Mathematics / Category Theory

• 📝 Toposes, Triples and Theories - Michael Barr, Charles Wells

• 📝 Abelian Categories - Peter Freyd

• 📝 Categories and Groupoids - P. J. Higgins

• 📝 Basic Concepts of Enriched Category Theory - G. M. Kelley

Algebra / Abstract Algebra

• 📝 Abstract Algebra : Theory and Applications - Thomas W. Judson, Robert A. Beezer (Austin State University)

Algebra / Group Theory

• 📝 Group Theory - Pedrag Civitanovic

Algebra / Linear Algebra

• 📝 Linear Algebra - David Cherney, Tom Denton, Andrew Waldron

• 📝 Introduction to vectors and tensors, Vol 1: linear and multilinear algebra - Ray M Bowen, C. C. Wang

• 📝 Introduction to vectors and tensors, Vol 2: vector and tensor analysis - Ray M Bowen, C. C. Wang

Geometry and Topology / Differential Geometry

• 📝 Semi-Riemann Geometry and General Relativity - Shlomo Sternberg

Analysis / Real Analysis

• 📝 Basic Analysis: Introduction to Real Analysis - Jiří Lebl

• 📝 Advanced Calculus - Lynn Loomis, Schlomo Sternberg

• 📝 Analysis of Functions of a Single Variable - Lawerence Baggett

• 📝 The Calculus of Functions of Several Variables - Dan Sloughter

• 📝 A ProblemText in Advanced Calculus - John M. Erdman

• 📝 Calculus and Linear Algebra. Vol. 1 - Wilfred Kaplan, Donald J. Lewis

• 📝 Calculus and Linear Algebra. Vol. 2 - Wilfred Kaplan, Donald J. Lewis

• 📝 Introduction to Calculus I and II - J.H. Heinbockel

• 📝 Active Calculus - Matt Boelkins

Analysis / Functional Analysis

• 📝 Functional Analysis - Lawerence Baggett

Analysis / Ordinary Differential Equations

• 📝 Difference Equations To Differential Equations - Dan Sloughter

• 📝 Notes on Differential Equations - Bob Terrell

• 📝 Elementary Differential Equations - William F. Trench

• 📝 Elementary Differential Equations With Boundary Value Problems - William F. Trench

• 📝 Notes on Diffy Qs: Differential Equations for Engineers - Jiří Lebl

Probability and Statistics / Statistics

• 📝 Rough set data analysis: A road to non-invasive knowledge discovery - Ivo Düntsch, Günther Gediga

Mathematics for Computer Science / Stochastic processes

• 📝 Mathematics for Computer Science - Eric Lehman, F. Thomson Leighton, Albert R. Meyer

• 📝 Algorithms and Complexity - H. Wilf

• 📝 Lecture Notes on Optimization - Pravin Varaiya

• 📝 Information Theory, Inference, and Learning Algorithms - David J. C. MacKay

Mathematical Biology / Stochastic processes

• 📝 Mathematical Biology - Jeffrey Chasnov

Mathematical Physics / Stochastic processes

• 📝 Introduction to Continuum Mechanics - Ray. M. Bowen

• 📝 Mathematical Tools for Physics - James Nearing

• 📝 Mechanism of the Heavens (1831) - Mary Somerville

Foundations of Mathematics / Transition To Pure Rigour Math

• 📝 Basic Concepts of Mathematics - Elias Zakon

Number Theory / Surreal Numbers

• 📝 An Introduction to the Theory of Numbers - Leo Moser

Algebra / Linear Algebra

• 📝 A First Courses in Linear Algebra - Rob Breezer

Algebra / Lie Algebras

• 📝 Lie Algebras - Shlomo Sternberg

Geometry and Topology / Graph Theory

• 📝 Mathematical Illustrations - Bill Casselman

Analysis / Real Analysis

• 📝 Elementary Calculus: An Approach Using Infinitesimals - Professor H. Jerome Keisler

• 📝 Mathematical Analysis Vol I - Elias Zakon

• 📝 Mathematical Analysis Vol II - Elias Zakon

Probability and Statistics / Statistics

• 📝 Concepts and Applications of Inferential Statistics - Richard Lowry

Books

• Multivariable Calculus - G. Cain, J. Herod (Georgia Tech)

Number Theory / Algebraic Number Theory

• 📝 A Course In Algebraic Number Theory - Robert Ash

Algebra / Analytic Number Theory

• 📝 A Course in Universal Algebra - S. Burris, H.P. Sankappanavar

• 📝 A Course in Commutative Algebra - Robert Ash

Algebra / Abstract Algebra

• 📝 Elements of Abstract and Linear Algebra - E.H. Connell (University of Miami)

• 📝 Abstract Algebra: The Basic Graduate Year - Robert Ash

Algebra / Linear Algebra

• 📝 Elementary Linear Algebra - Keith Matthews

Combinatorics / Lie Algebras

• 📝 generatingfunctionology - Herbert Wilf

Geometry and Topology / Graph Theory

• 📝 A=B - M. Petkovsek, H. Wilf, D. Zeilberger

• 📝 Elements - Euclid

• 📝 Euclid's Elements Redux - Daniel Callahan

Geometry and Topology / Differential Geometry

• 📝 The Geometry and Topology of Three-Manifolds - W. Thurston

Analysis / Real Analysis

• 📝 MIT OpenCourseWare Lectures on Calculus - G. Strang

Analysis / Complex Analysis

• 📝 Complex Analysis - G. Cain (Georgia Tech)

Analysis / Partial Differential Equations

• 📝 Linear Methods of Applied Mathematics - E. Harrell, J. Herod (Georgia Tech)

Probability and Statistics / Probability Theory

• 📝 An Introduction to Probability and Random Processes - Gian-Carlo Rota, Kenneth Baclawski

Books

• Trigonometry

Probability and Statistics / Statistics

• 📝 Theory of Statistics - James E. Gentle (George Mason University)

Probability and Statistics / Stochastic processes

• 📝 Lectures on Stochastic Processes - K. Ito (Tata Institute of Fundamental Research, Bombay)

• 📝 Probability and Stochastic Processes with Applications - Oliver Knill (Harvard University)

• 📝 Stochastic Processes - Amir Dembo (Stanford University)

• 📝 Lecture Notes on Stochastic Processes - Frank Noé, Bettina Keller and Jan-Hendrik Prinz (Freie Universität Berlin)

• 📝 Introduction to Stochastic Processes - Lecture Notes - Gordan Žitković (University of Texas)

• 📝 Applied Stochastic Processes in science and engineering - Matt Scott (University of Waterloo)

• 📝 An Introduction to Stochastic Processes in Continuous Time - Flora Spieksma (Leiden University)

• 📝 Markov Chains and Mixing Times - David A. Levin, Yuval Peres, Elizabeth L. Wilmer

Signal processing / Stochastic processes

• 📝 Introduction to Signal Processing - Sophocles J. Orfanidis (Rutgers University)

• 📝 Foundations of Signal Processing - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal

• 📝 An Introduction to Statistical Signal Processing - Robert M. Gray, Lee D. Davisson

• 📝 Linear algebra, signal processing, and wavelets. A unified approach. - Øyvind Ryan (University of Oslo)

Algebra / Linear Algebra

• 📝 Linear Algebra - Jim Hefferon

Blogs

• 3blue1brown - Animated Maths

Blogs

• BetterExplained - Maintained by Kalid Azad

• ILoveMaths - For grades 6 thru 12 in K-12 system

Books

• Beginning and Intermediate Algebra

Foundations of Mathematics / Surreal Numbers

• 📝 Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness - D. E. Knuth

• 📝 Surreal Numbers and Games

• 📝 Conway names, the simplicity hierarchy and the surreal number tree - Philip Ehrlich

Foundations of Mathematics / Logic

• 📝 An Introduction to Formal Logic - P.D. Magnus (University at Albany)

• 📝 Language, Proof, and Logic - Jon Barwise, John Etchemendy

Algebra / Group Theory

• 📝 Notes on Group Theory - Mark Reeder

Algebra / Linear Algebra

• 📝 Linear Algebra and Matrices - Martin Fluch

Analysis / Real Analysis

• 📝 Real Analysis for Graduate Students - Richard F. Bass

• 📝 Modern Real Analysis - William P. Ziemer (Indiana University)

Analysis / Complex Analysis

• 📝 Complex Analysis - Donald E. Marshall

Books

• Calculus: Basic Concepts for High Schools - L.V. Tarasov

Probability and Statistics / Probability Theory

• 📝 Probability and Statistics Cookbook (⭐2.3k) - Matthias Vallentin (UC Berkeley)

Encyclopedia

• ProofWiki

• Wolfram Mathworld

Probability and Statistics / Statistical Learning

• 📝 Reinforcement Learning: An Introduction - Richard S. Sutton, Andrew G. Barto

Algebra / Linear Algebra

• 📝 MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks (⭐568) - Juan Klopper

Learn to Learn

• Understanding Mathematics (⭐1.2k)

Probability and Statistics / Statistics

• 📝 NIST Handbook of Statistical Methods - Resource on practical statistics directed towards scientists and engineers.

Probability and Statistics / Statistics

• 📝 Statistics Papers - List of statistics papers curated by the Institute for Digital Research and Education (IDRE) at UCLA on methods such as bootstrap and factor invariance.

Books

• Online Mathematics Textbooks

Misc

• Paul's Online Math Notes - Paul Dawkins (Lamar University)

• List of electronic textbooks - Marcel B. Finan (Arkansas Tech University)

Probability and Statistics / Statistics

• 📝 Glossary of Data Modeling - AI Access

Probability and Statistics / Probability Theory

• 📝 The Only Probability Cheatsheet You'll Ever Need - William Chen

Learning Platforms

• Khan Academy

• Coursera

• MIT OpenCourseWare

• edX

Questions and Answers

• Mathematics Stack Exchange

• MathOverflow - for professional mathematicians

Encyclopedia

• Encyclopedia of Mathematics

• Planetmath

Books

• Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania)

• Wikibooks

Misc

• Areas of mathematics on Wikipedia

Foundations of Mathematics / Set Theory

• 📝 An Introduction to Set Theory - William A. R. Weiss

Foundations of Mathematics / Logic

• 📝 A Problem Course in Mathematical Logic - Stefan Bilaniuk (Trent University)

• 📝 Mathematical Logic - Helmut Schwichtenberg

• 📝 Mathematical Logic - Stephen G. Simpson (Pennsylvania State University)

• 📝 Formal Logic - Miguel Palomino

Foundations of Mathematics / Category Theory

• 📝 Introduction to Category Theory and Categorical Logic - Thomas Streicher

• 📝 An Introduction to Category Theory - Harold Simmons

Foundations of Mathematics / Homotopy Type Theory

• 📝 Homotopy Type Theory

Number Theory / Analytic Number Theory

• 📝 Elements of Analytic Number Theory - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)

• 📝 Analytic Number Theory - Lecture Notes based on Davenport’s book - Andreas Strömbergsson

Algebra / Abstract Algebra

• 📝 An Undergraduate Course in Abstract Algebra - Robert Howlett

Algebra / Group Theory

• 📝 Group Theory - J.S. Milne

• 📝 Notes on Finite Group Theory - Peter J. Cameron

Algebra / Linear Algebra

• 📝 Fundamentals of Linear Algebra - James B. Carrell

• 📝 Vector Space Theory - Robert Howlett

Algebra / Galois Theory

• 📝 Galois theory - Miles Reid

Combinatorics / Lie Algebras

• 📝 Applied Combinatorics - Mitchel T. Keller, William T. Trotter

• 📝 Notes on Combinatorics - Peter J. Cameron

• 📝 Analytic Combinatorics - Philippe Flajolet, Robert Sedgewick

Combinatorics / Graph Theory

• 📝 Graph Theory: Lecture Notes - Christopher Griffin

• 📝 Graph Theory - Reinhard Diestel

Geometry and Topology / Graph Theory

• 📝 Fundamentals of Geometry - Oleg A. Belyaev

Geometry and Topology / Differential Geometry

• 📝 Introduction to Differential Geometry - Joel W. Robbin, Dietmar A. Salamon

• 📝 Topics in Differential Geometry - Peter W. Michor

• 📝 Lectures on Differential Geometry - Wulf Rossmann

• 📝 An Introduction to Riemannian Geometry - Sigmundur Gudmundsson (Lund University)

Geometry and Topology / Algebraic Geometry

• 📝 Introduction to Algebraic Geometry - Igor V. Dolgachev

• 📝 Foundations of Algebraic Geometry - Ravi Vakil

• 📝 Algebraic Geometry - Jean Gallier, Stephen S. Shatz (University of Pennsylvania)

• 📝 Algebraic Geometry - J.S. Milne

• 📝 Algebraic Geometry - Andreas Gathmann (University of Kaiserslautern)

Geometry and Topology / Topology

• 📝 Introduction to Topology

• 📝 Introduction to Topology - Alex Küronya

• 📝 Introductory Topology - Jim L. Brown

• 📝 General Topology - Pierre Schapira (Paris VI University)

• 📝 Elementary Topology Problem Textbook

• 📝 General Topology - Jesper M. Møller

Geometry and Topology / Algebraic Topology

• 📝 Algebraic Topology - Allen Hatcher

• 📝 A Concise Course in Algebraic Topology - J. P. May

• 📝 Introduction to Algebraic Topology - Martin Cadek

• 📝 Algebra and Topology - Pierre Schapira (Paris VI University)

• 📝 Lecture Notes in Algebraic Topology - James F. Davis, Paul Kirk (Indiana University)

• 📝 Algebraic Topology - Michael Starbird

• 📝 Lecture Notes on Algebraic Topology - Jie Wu

Analysis / Real Analysis

• 📝 Introduction to Real Analysis - William F. Trench (Trinity University, Texas)

• 📝 Real Analysis - C. McMullen

Analysis / Functional Analysis

• 📝 Functional Analysis - Alexander C. R. Belton

Probability and Statistics / Probability Theory

• 📝 Introduction to Probability - Charles M. Grinstead, J. Laurie Snell

• 📝 Introduction to Probability - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT)

• 📝 A Short Introduction to Probability - Dirk P. Kroese (University of Queensland)

• 📝 Probability: Theory and Examples - Rick Durrett

Probability and Statistics / Statistics

• 📝 Lecture Notes on Statistical Theory - Ryan Martin (University of Illinois)

• 📝 Introduction to Statistics and Data Analysis for Physicists - Gerhard Bohm, Günter Zech

• 📝 Probability and Mathematical Statistics - Prasanna Sahoo (University of Louisville)

• 📝 Lectures on Statistics - William G. Faris

• 📝 Statistical Theory - Adolfo J. Rumbos

• 📝 Theory of Statistics - Joseph C. Watkins (University of Arizona)

Probability and Statistics / Statistical Learning

• 📝 An Introduction to Statistical Learning with Applications in R - Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani

• 📝 The Elements of Statistical Learning - Trevor Hastie, Robert Tibshirani, Jerome Friedman

Numerical Analysis / Stochastic processes

• 📝 A Concise Introduction to Numerical Analysis - Douglas N. Arnold (University of Minnesota)

• 📝 Numerical Analysis - L. Ridgway Scott

Foundations of Mathematics / Set Theory

• 📝 Set Theory and Foundations of Mathematics - Sylvain Poirier

• 📝 Set Theory on the Stanford Encyclopedia of Philosophy

Foundations of Mathematics / Category Theory

• 📝 Category Theory - Steve Awodey (Carnegie Mellon University)

• 📝 Category Theory - B. Pareigis

Number Theory / Surreal Numbers

• 📝 Elementary Number Theory: Primes, Congruences, and Secrets - William Stein

• 📝 A Course on Number Theory - Peter J. Cameron

• 📝 A Computational Introduction to Number Theory and Algebra - Victor Shoup

Number Theory / Algebraic Number Theory

• 📝 Algebraic Number Theory - J.S. Milne

• 📝 Algebraic Number Theory Course Notes - Matthew Baker (Georgia Tech)

Number Theory / Analytic Number Theory

• 📝 Introduction to Analytic Number Theory - A.J. Hildebrand (University of Illinois)

• 📝 Analytic Number Theory - Otto Forster (LMU Munich)

Algebra / Abstract Algebra

• 📝 Introduction to Modern Algebra - David Joyce (Clark University)

Algebra / Ring Theory

• 📝 Foundations of Module and Ring Theory - Robert Wisbauer (University of Düsseldorf)

Algebra / Galois Theory

• 📝 An Introduction to Galois Theory - Andrew Baker (University of Glasgow)

• 📝 Fields and Galois Theory - J.S. Milne

Analysis / Real Analysis

• 📝 An Introduction to Real Analysis - John K. Hunter (University of California at Davis)

• 📝 Elementary Real Analysis - Thomson, Bruckner

• 📝 Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University)

Analysis / Harmonic Analysis

• 📝 Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana–Champaign)

• 📝 Harmonic Analysis - W. Schlag

• 📝 Lecture Notes: Fourier Transform and its Applications - Brad Osgood

• 📝 Fourier Analysis - Lucas Illing

Analysis / Complex Analysis

• 📝 An Introduction to Complex Analysis and Geometry - John P. D'Angelo (University of Illinois)

• 📝 A First Course in Complex Analysis - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka

• 📝 A Guide to Complex Variables - Steven G. Krantz

• 📝 Complex Analysis - Charles Walkden

• 📝 Complex Analysis - Christian Berg

• 📝 Complex Variables - R. B. Ash, W.P. Novinger

• 📝 Complex Analysis - Christer Bennewitz

Analysis / Functional Analysis

• 📝 Functional Analysis: Lecture Notes - Jeff Schenker (Michigan State University)

• 📝 Topics in Real and Functional Analysis - Gerald Teschl

• 📝 Functional Analysis - Christian Remling

Analysis / Measure Theory

• 📝 Lecture Notes on Measure Theory and Functional Analysis - P. Cannarsa, T. D’Aprile

• 📝 Lecture Notes in Measure Theory - Christer Borell

• 📝 A Crash Course on the Lebesgue Integral and Measure Theory - Steve Cheng

• 📝 Measure Theory - John K. Hunter (University of California at Davis)

• 📝 Measure and Integration - Dietmar A. Salamon (ETH Zürich)

• 📝 Lecture notes: Measure Theory - Bruce K. Driver

Analysis / Ordinary Differential Equations

• 📝 Ordinary Differential Equation - Alexander Grigorian (University of Bielefeld)

• 📝 Ordinary Differential Equations: Lecture Notes - Eugen J. Ionascu

• 📝 Ordinary Differential Equations - Peter Philip

• 📝 Ordinary Differential Equations - Gabriel Nagy

• 📝 Ordinary Differential Equations and Dynamical Systems - Gerald Teschl

Analysis / Partial Differential Equations

• 📝 Notes on Partial Differential Equations - John K. Hunter (University of California at Davis)

• 📝 Partial Differential Equations: Lecture Notes - Erich Miersemann (Leipzig University)

Probability and Statistics / Statistical Learning

• 📝 Statistical Learning Theory - Percy Liang