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

Number Theory

Number Theory: A Contemporary Introduction - Pete L. Clark

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

Foundations of Mathematics

Logic

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

Geometry and Topology

Topology

Topology Topics

Analysis

Complex Analysis

Introduction to Complex Analysis - Michael Taylor

Students Lecture Notes

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.

Foundations of Mathematics

Transition To Pure Rigour Math

Book of Proof - Richard Hammak (Virginia Commonwealth University)

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)

Algebra

Understanding Algebra - James W. Brennan

Foundations of Mathematics

Type Theory

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

Tools

GeoGebra

Macaulay2

Singular

GNU Octave

Magma

Maple

Matlab

Wolfram Mathematica

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

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

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)

Foundations of Mathematics

Logic

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

Learning Platforms

Mathigon

Misc

Convex Optimization - Stephen Boyd and Lieven Vandenberghe

Algebra

Linear Algebra

Interactive Linear Algebra - Dan Margalit and Joseph Rabinoff

Linear Algebra, Infinite Dimensions, and Maple - James Herod

Geometry and Topology

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

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

Books

Free Mathematics Books

Blogs

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

Signal processing

Think DSP - Allen B. Downey

Algebra

Galois Theory

Galois Theory - Ian Stewart

Foundations of Mathematics

Type Theory

Type Theory and Functional Programming - Simon Thompson

Foundations of Mathematics

Type Theory

Intuitionistic Type Theory - Per Martin-Lof

Proofs and Types - Jean-Yves Girard

Number Theory

Elementary Number Theory - David M. Burton

Tools

Unit Converter

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)

Analysis

Functional Analysis

Theory of Functions of a Real Variable - Shlomo Sternberg

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

Learning Platforms

WooTube

Brilliant

Blogs

Mathsisfun simple text light weight site for students upto highschool

Youtube Series

Brandon Foltz

3blue1brown

NPTEL

Prof. Leonard

Crash Course

Harvard

MIT

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

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

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

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

Numerical Analysis

Numerical Analysis for Engineers - Douglas Wilhelm Harder

Foundations of Mathematics

Logic

Mathematical Reasoning: Writing and Proof - Ted Sundstrom

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

Predictive Arithmetic - Edward Nelson

Number Theory

Yet Another Introductary Number Theory Textbook - Jonathan A. Poritz

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

Analysis

Real Analysis

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

Basic Analysis: Introduction to Real Analysis - Jiří Lebl

A ProblemText in Advanced Calculus - John M. Erdman

Analysis of Functions of a Single Variable - Lawerence Baggett

Advanced Calculus - Lynn Loomis, Schlomo Sternberg

The Calculus of Functions of Several Variables - Dan Sloughter

Mathematics for Computer Science

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

Mathematical Biology - Jeffrey Chasnov

Mathematical Physics

Introduction to Continuum Mechanics - Ray. M. Bowen

Mathematical Tools for Physics - James Nearing

Mechanism of the Heavens (1831) - Mary Somerville

Analysis

Ordinary Differential Equations

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

Notes on Differential Equations - Bob Terrell

Difference Equations To Differential Equations - Dan Sloughter

Foundations of Mathematics

Category Theory

Abelian Categories - Peter Freyd

Categories and Groupoids - P. J. Higgins

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

Toposes, Triples and Theories - Michael Barr, Charles Wells

Analysis

Functional Analysis

Functional Analysis - Lawerence Baggett

Foundations of Mathematics

Set Theory

Sets, Relations, Functions - Ivo Düntsch, Günther Gediga

Geometry and Topology

Differential Geometry

Semi-Riemann Geometry and General Relativity - Shlomo Sternberg

Probability and Statistics

Statistics

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

Foundations of Mathematics

Transition To Pure Rigour Math

Basic Concepts of Mathematics - Elias Zakon

Number Theory

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

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

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

Linear Algebra - Jim Hefferon

Elementary Linear Algebra - Keith Matthews

Combinatorics

generatingfunctionology - Herbert Wilf

Geometry and Topology

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)

Signal processing

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)

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

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

An Introduction to Surreal Numbers - Gretchen Grimm

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 - 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 Notebooksstars426 - Juan Klopper

Learn to Learn

Understanding Mathematicsstars651

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

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

Algebraic Methods - F. Oggier

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

Linear Algebra - Peter Petersen

Algebra

Galois Theory

Galois theory - Miles Reid

Geometry and Topology

Differential Geometry

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

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

Topics in Differential Geometry - Peter W. Michor

Lectures on Differential Geometry - Wulf Rossmann

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

Analysis

Real Analysis

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

Real Analysis - C. McMullen

Analysis

Functional Analysis

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

Functional Analysis - Alexander C. R. Belton

Analysis

Measure Theory

An Introduction to Measure Theory - Terence Tao (UCLA)

Combinatorics

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

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

Fundamentals of Geometry - Oleg A. Belyaev

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

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

Numerical Analysis

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

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

Numerical Analysis - L. Ridgway Scott

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

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

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

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)

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

Functional Analysis

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

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

Topics in Real and Functional Analysis - Gerald Teschl

Functional Analysis - Christian Remling

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

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

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)

Number Theory

Algebraic Number Theory

Introduction to Algebraic Number Theory - F. Oggier

Introduction to Algebraic Number Theory

Algebraic Number Theory - J.S. Milne

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

Algebra

Ring Theory

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

Foundations of Mathematics

Category Theory

Category Theory - Steve Awodey (Carnegie Mellon University)

Category Theory - B. Pareigis

Algebra

Galois Theory

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

Fields and Galois Theory - J.S. Milne

Algebra

Abstract Algebra

Introduction to Modern Algebra - David Joyce (Clark University)

Probability and Statistics

Statistical Learning

Statistical Learning Theory - Percy Liang

Number Theory

Analytic Number Theory

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

Analytic Number Theory - Otto Forster (LMU Munich)

Foundations of Mathematics

Set Theory

Set Theory on the Stanford Encyclopedia of Philosophy

Set Theory and Foundations of Mathematics - Sylvain Poirier

Number Theory

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