Textbooks in Mathematics

Looking for Textbooks in Mathematics?

A list of links to useful mathematical textbooks available for free on the Internet.
They are all legal and maintained by their authors or by the legitimate publisher.

All the documents are in English. They are in a printable format - Postscript
or Adobe Portable Document Format. You are free to download, read and print them.
Here are some links to other sites offering lists of free mathematical textbooks.

For any comments, please, contact me: alex_stef@yahoo.com

Remark: indicates a book for which there is also a printed version
indicates documents which appear for first time in the current edition of this page.

Topics in mathematics General Foundations Number theory Discrete mathematics Mathematicians History of mathematics Philosophy of mathematics Mathematical notation Mathematical beauty Mathematics education Areas of mathematics Foundations of mathematics Set theory Naive set theory Axiomatic set theory Mathematical logic Proof theory Model theory Category theory Topos theory Gödel's incompleteness theorems Number theory Algebraic number theory Analytic number theory Arithmetic Numbers Natural numbers Prime numbers Rational numbers Algebraic numbers Fundamental theorem of arithmetic Discrete mathematics Combinatorics Graph theory Game theory Discrete geometry Theoretical computer science Computability theory Complexity theory Information theory Analysis Algebra Geometry and topology Applied mathematics Analysis Calculus Vector calculus Differential equations Calculus of variations Real analysis Complex analysis Functional analysis Harmonic analysis Measure theory Special functions Trigonometry Fundamental theorem of calculus Algebra Elementary algebra Abstract algebra Group theory Ring theory Field theory Commutative algebra Linear algebra Matrix theory Multilinear algebra Universal algebra Order theory Fundamental theorem of algebra Geometry Topology General topology Algebraic topology Geometric topology Euclidean geometry Non-Euclidean geometry Affine geometry Projective geometry Differential geometry Riemannian geometry Lie groups Algebraic geometry Four color theorem Pythagorean theorem Applied mathematics Numerical analysis Mathematical biology Optimization Dynamical systems Chaos theory Financial mathematics Cryptography Mathematical physics Classical mechanics Probability Statistics Operations research edit   Index of mathematics articles ARTICLE INDEX: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 0-9 MATHEMATICIANS: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z edit   Related portals Geometry Physics Science Computer science Cryptography

New documents

A First Course in Linear Algebra by Robert A. Beezer (GNU Free Documentation License)

General Mathematics

• Mathematical Logic - an Introduction by Michal Walicki
• Set theory by Dr. P. G. Dixon
• Mathematical Logic by Stephen G. Simpson
• Foundations of Mathematics by Stephen G. Simpson
• Model Theory by Stephen G. Simpson
• The theory of the foundations of mathematics - 1870 to 1940
• A Problem Course in Mathematical Logic by Stefan Bilaniuk
• Computability and Incompleteness by Jeremy Avigad
• Complete proofs of Gödel's Incompleteness Theorems
• Fundamentals of Model Theory by William Weiss and Cherie D'Mello

For more logic lecture notes go to: ASSOCIATION FOR SYMBOLIC LOGIC members.
For more set theory materials go to: Set Theory Preprint Sites

• Lecture Notes on Discrete Mathematics by László Lovász

• Algebraic Groups and Discontinuous Subgroups by Armand Borel and George D. Mostow
• Theory of representations etc. by Claudio Procesi
• Semisimple Lie Algebras and their Representations, by Robert N. Cahn,
• Linear Algebraic Groups - minor thesis by David Dumas

• Textbook in Problems on Elementary Topology by O.Ya.Viro, O.A.Ivanov, V.M.Kharlamov and N.Y.Netsvetaev unfinished
• Topology Course Lecture Notes by Aisling McCluskey and Brian McMaster
• Topology lecture notes(3rd year) by Thomas Ward
• Foliations and the topology of 3-manifolds by Danny Calegari

• Allen Hatcher's homepage has a (nearly complete) textbook.
• Introduction to Sheaf Theory and Algebraic Topology, by Pierre Schapira
• Cohomology, Connections, Curvature and Characteristic Classes by David Mond
• Introduction to Characteritic Classes and Index Theory by Jean-Pierre Schneiders

• Algebraic Topology by Solomon Lefschetz, AMS 1942, 389 pp.
• Abstract group theory and topology articles by Walter Neumann

• An introduction to algebraic K-theory, by Charles Weibel.

• Classical Knot Theory by C. Kearton
• Knots Knotes. by J. D. Roberts
• Vassiliev invariants and combinatorial structures by S.V.Duzhin
• Introduction to Vassiliev knot invariants by S.Chmutov, S.Duzhin

• Homeomorphisms in Analysis by Casper Goffman, Togo Nishiura, and Daniel Waterman
• Why the Boundary of a Round Drop Becomes a Curve of Order Four by A. N. Varchenko and P. I. Etingof
• Lectures on Entire Functions by B. Ya. Levin
• Constructive Real Numbers and Constructive Function Spaces by N. A. Sanin
• Complex Variables by Robert B. Ash and W.P. Novinger
• Foundations of Nonstandard Analysis by Erland Gadde
• Analytic functions by Stanislaw Saks, Antoni Zygmund

• Functional Analysis by Douglas N. Arnold
• Paul Garrett's lecture notes
• Functional Analysis (3rd year) lecture notes by Thomas Ward
• Functional Analysis and Semi-Groups by Einar Hille and R. S. Phillips, AMS 1957, 808 pp
• The Convenient Setting of Global Analysis by Andreas Kriegl and Peter W. Michor, AMS 1997, 618pp
• Hilbert Space Methods for Partial Differential Equations, by R.E. Showalter
• Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, by R. E. Showalter
• Harmonic Analysis and Partial Differential Equations - Björn E.J. Dahlberg and Carlos E. Kenig
• Functional Analysis by Thomas Ward
• Harmonic Function Theory by Sheldon Axler, Paul Bourdon, and Wade Ramey printing disabled
• An Introduction to C*-Algebras by Pierre de la Harpe and Vaughan Jones
• Functional Analysis by Dr. P. G. Dixon
• Introduction to Microlocal Analysis by Richard Melrose

• Fourier Integrals by Victor Palamodov
• Reconstruction of image from projections by Victor Palamodov
• Bernoulli Periodic distributions Notes by Miguel Lerma
• Holomorphic Methods in Analysis and Mathematical Physics by Brian C. Hall

• Introduction to Tensor Calculus and Continuum Mechanics, by John H. Heinbockel
• Topics in Differential Geometry, Peter W. Michor.
• Natural operations in differential geometry by Ivan Kolar, Jan Slovak and Peter W. Michor
• Intrinsic Geometry of Surfaces by A. D. Aleksandrov and V. A. Zalgaller
• An Introduction to Riemannian Geometry - Sigmundur Gudmundsson, Lund University
• Riemann Surfaces, Dynamics and Geometry Curtis McMullen
• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem by Peter B. Gilkey
• Differentiable Manifolds lecture notes (growing) by Mariusz Wodzicki
• Lecture notes for the course in Differential Geometry by Sergei Yakovenko
• Lectures On Symplectic Geometry with and Eye Toward Combinatorics by Sue Tolman
• Differential Geometry lecture notes by Gabriel Lugo
• Differential geometry reconstructed by Alan U. Kennington
• Course of Differential Geometry by Ruslan Sharipov
• A Modern Course on Curves and Surfaces by Richard S. Palais
• Undergraduate notes on Projective Geometry, Manifolds etc. by Nigel Hitchin
• Vector Bundles and an Introduction to Gauge Theory by Steven Bradlow, (Hung-Jen Hsu and Chris Willett)
• Twistor Geometry and Gauge Theory by Martin Wolf
• Complex Geometry of Nature and General Relativity by Giampiero Esposito

• Geometric Asymptotics by Victor Guillemin and Shlomo Sternberg
• Projective Geometry by Balázs Csikós
• Differential Geometry by Balázs Csikós
• Projective and Polar Spaceas by Peter Cameron
• Transformation groups for begginers by S. V. Duzhin and B. D. Tcherbotarevsky

• Comprehensive textbook on quantum (and classical) field theory by Warren Siegel
• Quantum Field Theory by Ben Simons
• Mathematical ideas and notions of quantum field theory by Pavel Etingof
• Introduction to Algebraic and Constructive Quantum Field Theory by John C. Baez, Irving E. Segal and Zhengfang Zhou scanned pdf. extermely big 200 megabytes
• Lecture Notes from the Quantum Field Theory program at IAS, 1996-1997
• Books by Warren Siegel
• Introduction to String Theory by Igor V. Dolgachev
• What is String Theory by Joseph Polchinski
• Fluctuating Geometries in Statistical Mechanics and Field Theory Les Houches Session LXII
• Introduction to Superstring Theory by Elias Kiritsis
• Operator Algebras and Quantum Statistical Mechanics, Volumes I & II by Ola Bratteli
• D-Brane Primer by Clifford V. Johnson
• Introduction to Superstring Theory by Elias Kiritsis

• Introduction to Solid-State Physics; Many-Body Theory by Chetan Nayak
• Concepts of Theoretical Solid State Physics by Alexander Altland
• Many-Body Physics by Piers Coleman
• Theory of Superconductivity by Helmut Eschrig
• High-Temperature Superconductivity by Peter Hirschfeld
• Solid State Physics Notes, Problem Sets, & Tests by Peter Hirschfeld
• Complex Surphaces in Materials Science with few books

• Special Relativity on the World Wide Web. Tutorials, lecture notes, and computer simulations.
• Mechanics and Special Relativity introductiry textbook by David Morin
• SERGIU KLAINERMAN General Relativity, Nonlinear PDEs, etc.
• Special Relativity and Geometry by C. E. Harle, R. Bianconi
• Differential Geometry (and Relativity) notes by Bob Gardner
• Lecture Notes on General Relativity by Sean M. Carroll
• General Relativity and Quantum Cosmology by Sean M. Carroll
• Public lectures by Stephen Hawking and Roger Penrose

• Essential Physics 1 by Frank Firk
• Introduction to Groups, Invariants & Particles by Frank W.K. Firk
• Classical Electrodynamics by Bo Thidé
• Classical electrodynamics and theory of relativity by Ruslan Sharipov
• Electromagnetic Theory and Computation: A Topological Approach by Paul W. Gross and P. Robert Kotiuga
• MOTION MOUNTAIN TEXTBOOK Hiking beyond space and time along the concepts of modern physics by Christoph Schiller
• Fundamentals of Thermodynamics by J. Karl Johnson
• Non-Equilibrium Statistical Mechanics by Klaus Schulten
• Course in Electrodynamics by Franz Wegner
• Light and Matter by Ben Crowell
• Order-of-magnitude-physics a book by Sanjoy Mahajan
• A Brief Introduction to Physics for Mathematicians, Igor V. Dolgachev
• Physical Applications of Geometric Algebra by Anthony Lasenby and Chris Doran
• Group Theory for Physicists by Predrag Cvitanovic'
• An Elementary Introduction to Groups and Representations by Brian C. Hall
• Geometric Models for Noncommutative Algebras by A. Cannas da Silva and A. Weinstein
• Teaching electromagnetic field theory using differential forms by K.Warnick,R.Selfridge and D.Arnold
• Lectures on integration of several variables by Michael Adler
• Methods of Mathematical Physics by Mark Trodden
• Concepts in Theoretical Physics by Ben Simons
• Further Mathematical Methods by Niels Walet
• Computational Physics by Angus MacKinnon

Traveling Wave Solutions of Parabolic Systems by Aizik I. Volpert, Vitaly A. Volpert, and Vladimir A. Volpert, AMS 1994, 455 pp.

Introduction to Probability, by Charles Grinstead & J. Laurie Snell

Probability, Random Processes, and Ergodic Properties by R.M. Gray

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Applied Mathematics

• Information Theory, Inference and Learning Algorithms. A Textbook by David J.C. MacKay
• A Short Course in Information Theory - 8 lectures by David J.C. MacKay
• Primer on Information Theory by Thomas Schneider
• Several books ! by G. J. Chaitin (not only Information Theory)

• Applied Quantitative Finance by W. Härdle, T. Kleinow, G. Stahl printing disabled
  Also other non-printable books on the same page
• Measure theory, Probability, Stochastic calculus, General theory of processes, Financial mathematics lectures notes by Rich Bass
• Lectures on Stochastic Calculus and Finance by Steven Shreve
• Structural Analysis of Discrete Data and Econometric Applications, editors: Ch. Manski, D. McFadden
• Handbook of Econometrics, editiors: J. J. Heckman, E. Leamer and R. Blundell
• Essential Principles of Economics by Roger McCain
• Game theory examples by Roger McCain (html)

• Gametheory.net with lectures on the subject
• Determinacy in infinite games by Jindrich Zapletal

generatingfunctionology by Herbert Wilf

Algorithms and Complexity by Herbert S. Wilf

A=B by Marko Petkovsek, Herbert Wilf, and Doron Zeilberger

• Handbook of Applied Cryptography, by Alfred J. Menezes , Paul C. van Oorschot, and Scott A. Vanstone
• Foundations of Cryptography
• Lecture Notes on Cryptography
• Cryptography and Network Security
• Cryptography and Cryptanalysis Lecture notes
• Modern Cryptography
• Cryptography and Cryptanalysis by Glenn Durfee
• Lecture Notes on Cryptography by S. Goldwasser and M. Bellare

• Introduction to Statistical Signal Processing by R.M. Gray and L.D. Davisson

• Fractals in the Plane - the Ergodic Theory Methods by F. Przytycki and M. Urbanski
• Lecture notes in Conformal Dynamics, taught by Curt McMullen.
• Fractals by Dr. P. G. Dixon

• Graph Theory with Applications by J.A. Bondy and U.S.R. Murty
• Graph Theory by Reinhard Diestel printing disabled
• Interactive Graph theory tutorials by Chris K. Caldwell must register to use

• Mirrors and Reflections: The Geometry of Finite Reflection Groups by Alexandre V. Borovik, Anna s. Borovik
• Miscellaneous facts about Coxeter groups by Robert B. Howlett
• Buildings, BN-pairs, Hecke algebras, classical groups by Paul Garrett

• Ross Geoghegan's Home Page has a set of papers

• Mathematics of Rubik's cube by David Joyner is a good source for discrete group theory with applications to permutation puzzles.

How to prepare documents? TEX,LATEX etc.

• Formatting information - A beginner's introduction to typesetting with LaTeX by Peter Flynn
• TeX by Topic the TeXbook of Victor Eijkhout
• LaTeX2e for authors
• Mathematical Illustrations, a manual of geometry and postscript by Bill Casselman

• The TeXbook by Donald Knuth is the most comrehensive book about TEX (tex source)
• The METAFONTbook is also downloadable (tex source)
  The last two books are copyrighted and you are not supposed to compile them. These files are, in fact, much more than sources of textbooks. They are invaluable examples of TeX input.

To view search results about textbooks, click here.

General	Foundations	Number theory	Discrete mathematics
Mathematicians History of mathematics Philosophy of mathematics Mathematical notation Mathematical beauty Mathematics education Areas of mathematics	Foundations of mathematics Set theory Naive set theory Axiomatic set theory Mathematical logic Proof theory Model theory Category theory Topos theory Gödel's incompleteness theorems	Number theory Algebraic number theory Analytic number theory Arithmetic Numbers Natural numbers Prime numbers Rational numbers Algebraic numbers Fundamental theorem of arithmetic	Discrete mathematics Combinatorics Graph theory Game theory Discrete geometry Theoretical computer science Computability theory Complexity theory Information theory
Analysis	Algebra	Geometry and topology	Applied mathematics
Analysis Calculus Vector calculus Differential equations Calculus of variations Real analysis Complex analysis Functional analysis Harmonic analysis Measure theory Special functions Trigonometry Fundamental theorem of calculus	Algebra Elementary algebra Abstract algebra Group theory Ring theory Field theory Commutative algebra Linear algebra Matrix theory Multilinear algebra Universal algebra Order theory Fundamental theorem of algebra	Geometry Topology General topology Algebraic topology Geometric topology Euclidean geometry Non-Euclidean geometry Affine geometry Projective geometry Differential geometry Riemannian geometry Lie groups Algebraic geometry Four color theorem Pythagorean theorem	Applied mathematics Numerical analysis Mathematical biology Optimization Dynamical systems Chaos theory Financial mathematics Cryptography Mathematical physics Classical mechanics Probability Statistics Operations research