To the best of my knowledge, all these books were made available on Internet in a legal way (else, please, let me know).
The links are checked about once a month and any broken ones are eliminated.
Thanks to all who share their knowledge for free with all of us.


Regular BOOKS 
about mathematics and related topics

Online COURSES 
Lecture Notes and Textbooks

Doctoral and Master THESES 
about mathematical topics



Authors, please, let me know the link to your document, so I can list it here.
If the document is not yet on the Interned, let me know anyway and I will host it on this site for free.

You might wish to consult also other lists and collections
Particularly recommended: Project Gutenberg math section.
Free, online MATHEMATICS BOOKS
 A New Kind of Science by Stephen Wolfram (first printed in 2002).
Software, math and physics. Pagebypage access.
 A = B, a book about combinatorial identities
by Marko Petkovsek, Herbert S.Wilf and Doron Zeilberger.
 A Companion to Real Analysis by John M.Erdman.
 A Computational Introduction to Number Theory and Algebra by Victor Shoup.
 Abelian Categories by Peter Freyd.
 Abstract and concrete categories: The joy of cats
by Jiri Adamek, Horst Herrlich and George Strecker. Alternative source.
 Advanced Calculus (! 58 MB), by Lynn Loomis and Shlomo Sternberg.
 Algebraic Topology, Vol.I, by Allen Hatcher. Available also in printed version.
 Algorithms and Complexity by Herbert S. Wilf. Buy 2nd Edition.
 Arithmetic Duality Theorems by James S.Milne.
Available also in printed form.
 Asynchroneous Systems Theory by Serban E.Vlad. Published by WSEAS.
 Automorphic Forms, Shimura Varieties, and Lfunctions, Volumes I and II.
Proceedings of a Conference held at the University of Michigan, Ann Arbor, July 616, 1988.
Edited by L.Clozel and James S.Milne.
 Basic Bundle Theory and KCohomology Invariants,
by D.Husemöller et al. Available also in printed version
 Basic Concepts of Enriched Category Theory by G.M.Kelly.
 Basic Concepts of Mathematics by Elias Zakon
made available by the Trillia Group.
 Calculus Without Limits by John C.Sparks.
 Categories and Groupoids by P.J.Higgins.
 Combinatorial and Computational Geometry, a 2005 collection of articles
edited by Jacob E. Goodman, János Pach and Emo Welzl.
Available also in print
 Complex Variables by Robert B. Ash and Phil Novinger.
 Complex Analysis by George Cain.
 Concepts and Applications of Inferential Statistics by Richard Lowry.
 Concise Encyclopedia of Mathematics by Eric Weisstein.
1998 version available also in print and on CD.
 Conditional Rate Distortion Theory by Robert M.Gray.
Scanned copy of Information Systems Laboratory Technical Report 65022, October 1972.
 Convergence of Stochastic Processes by David Pollard.
 Convex Optimization by Stephen Boyd and Lieven Vandenberghe.
Available also in print.
Original Edition Cambridge University Press 2004.
 Difference Equations to Differential Equations by Dan Sloughter.
 DOE Fundamentals Handbook, Mathematics:
Vol.1,
Vol.2,
 Dynamical Systems by Shlomo Sternberg.
 Dynamics in One Complex Variable by John Milnor.
1st Edition, IMS 1990. Also available: Printed 3rd Edition.
 Dynamics, Ergodic Theory, and Geometry, a 2007 collection of articles
edited by Boris Hasselblatt.
Available also in print
 E Infinity Ring Spectra and E Infinity Ring Spaces
by J.Peter May et al (Springer 1977).
Available also in printed version.
 Elementary Calculus: An Approach Using Infinitesimals by H.J.Keisler.
 Elementary Number Theory by William Stein.
 Elementary Real Analysis by Thomson B.S., Bruckner J.B. and Bruckner A.M..
ChapterbyChapter downloads are close to the page bottom.
See also. Available also in printed version.
 Elements of Abstract and Linear Algebra by Edwin H. Connell.
 Elliptic Curves by James S.Milne.
Available also in printed form.
 Euclid's Elements edited by David E.Joyce.
 Equivariant Stable Homotopy Theory
by L.G.Jr.Lewis, J.P.May,
M.Steinberger, J.E.McClure (Springer 1986).
Available also in printed version.
 Finite Element Methods by Nikos Mastorakis and Olga Martin. Published by WSEAS.
 Foundations of Combinatorics with Applications
by Edward A. Bender and Gill S. Williamson.
 Foundations of Differentiable Manifolds and Lie Groups
by Frank W.Warner. In DjVu format.
Available also in print.
 Generatingfunctionology, 2nd Ed., by J.Wilf, and the publisher, A.K.Peters.
 Geometric Asymptotics by Shlomo Sternberg, on AMS Online
 Graph Algorithms by Shimon Evan (Chapters 16, .ps format).
more >>.
 Graph Theory by R.Diestel.
Available also in printed version.
 Graph Theory with Applications by J.A. Bondy and U.S.R. Murty.
 Group Characters, Symmetric Functions, and the Hecke Algebra
by David M.Goldschmidt.
AMS 1993. Available also in printed version.
 Group Theory by Predrag Cvitanovic'.
 H Infinity Ring Spectra and their Applications
by R.R.Brunner, J.P.May,
J.E.McClure, M.Steinberger (Springer 1986).
Available also in printed version.
 Handbook of Mathematical Functions by M.Abramowitz and A.Stegun, Editors.
 Hodge Cycles, Motives, and Shimura Varieties by Pierre Deligne,
James S.Milne, Arthur Ogus and Kuangyen Shih.
Available also in printed form.
 Information Theory, Inference, and Learning Algorithms, by David MacKay.
Available also in print.
 Introduction to Bayesian Statistics by H.Thornburg.
 Introduction to Matrix Algebra by Autar Kaw. Alternative source at Scribd.
 Introduction to Probability Theory by Charles M.Grinstead and J.Laurie Snell.
GNU License. Acompanied by a number of tools and links.
Available also in print.
 Introduction to Probability and Random Processes
by GianCarlo Rota and Kenneth P.Baclawski.
 Introduction to Real Analysis by William Trench.
PDF shortcut
and an alternative.
 Introduction to Statistical Data Processing by R.M.Gray and L.D.Davisson.
Courtesy Cambridge University Press. Available also in printed version.
 Introduction to the Theory of Numbers by Leo Moser
by courtesy of Trillia Group.
 Introduction to Vectors and Tensors,
Vol.1: Linear and Multilinear Algebra and Vol.2: Vector and Tensor Analysis
by Ray M. Bowen and C.C. Wang. 1st Edition Plenum Press 1976; Updated 2008.
 Inverse Problem Theory and Methods for Model Parameter Estimation
by Albert Tarantola,
SIAM 2005. Available also in printed form.
 Jacobi Operators and Completely Integrable Nonlinear Lattices by Gerald Teschl.
Available also in printed form.
 Lie Algebras by Shlomo Sternberg.
 Linear Algebra, a nice undergraduate book by Jim Hefferon (Saint Michaels' College).
 Linear Algebra, Infinite Dimensions, and Maple, an online book by Jim Herod.
 Linear Controller Design  Limits of Performance
by Stephen Boyd and Craig Barratt. Original Edition Prentice Hall 1991.
 Linear Matrix Inequalities in System and Control Theory
by Stephen Boyd, Laurent El Ghaoui, Eric Feron, and Ragu Balakrishnan.
Available also in print. Original Edition SIAM 1997.
 Linear Methods of Applied Mathematics by E.M.Harrell II and J.Herod.
 Linear Partial Differential Equations and Fourier Theory by Marcus Pivato.
 Logic for Computer Science: Foundations of Automatic Theorem Proving
by Jean Gallier. Wiley 1986. Revised 2003.
 Mapping of Probabilities  Theory for the Interpretation of Uncertain Physical Measurements, an online book by Albert Tarantola.
In preparation; only the first two Chapters are finished.
 Mathematical Analysis I by Elias Zakon
made available by the Trillia Group.
 Mathematical Analysis II by Elias Zakon
made available by the Trillia Group.
 Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications, J.O.Smith III.
 Multivariable Calculus by George Cain and James Herod.
 My Algebra Book by Eric Kean. A nice college algebra initiative.
 Notes on Differential Geometry by Noel J.Hicks (1965).
 Number Theory, an undergraduate revision by Jim Hefferon of a text by W.E.Clark.
 Practical Foundations of Mathematics by Paul Taylor.
Available also in print
 Predicative Arithmetic by Edward Nelson.
 Probability, geometry, and integrable systems, a 2008 collection of articles
edited by Mark Pinsky and Björn Birnir.
Available also in print
 Probability, Random Processes, and Ergodic Properties by R.M.Gray.
 Radically Elementary Probability Theory by Edward Nelson.
 Real Analysis by Bruckner J.B., Bruckner A.M. and Thomson B.S..
Partial free download and a
printed version.
 Real Variables with Basic Metric Space Topology by Robert B. Ash.
Originally published by IEEE Press in 1992, ISBN 078030408X. 78 Mb pdf.
 Rough Set Data Analysis: A road to noninvasive knowledge discovery,
a primer by Ivo Düntsch and Günther Gediga.
Available also in print
 Semiriemannian Geometry by Shlomo Sternberg.
 Sequential Simplex Optimization (PDF 3.8 Mb) by Walters F.H., Morgan S.L., Parker L.R.Jr., Deming S.N., CRC Press 1991. Licensed electronic reprint 1999.
 Seminar on Triples and Categorical Homology Theory,
edited by Beno Eckmann and Myles Tierney.
 Sets, Relations, Functions, a primer by Ivo Düntsch and Günther Gediga.
More >>.
 Simple Groups of Finite Morley Rank
by Tuna Altinel, Alexandre V. Borovik, and Gregory Cherlin. Early version of AMS 2008.
 Spectral Sequences in Algebraic Topology by Allen Hatcher.
 Statistics: Methods and Applications by Thomas Hill and Paul Lewicki at StatSoft.
Available also in print.
 StatLect  Lectures on Probability and Statistics by Marco Taboga. Very good.
 Tensor Analysis by Edward Nelson.
 The Geometry and Topology of ThreeManifolds by William Thurston.
 The Calculus Bible by G.S.Gill.
 The Calculus of Functions of Several Variables by Dan Sloughter.
 The Geometry of Iterated Loop Spaces by J.Peter May.
 The Homology of Iterated Loop Spaces
by Frederick R.Cohen, Thomas J.Lada and J.Peter May.
Available also in print.
 The Matrix Cookbook, a free mathematical desktop reference on matrices
by Kaare B.Petersen and Michael S.Pedersen.
 Theory of Functions of a Real Variable by Shlomo Sternberg.
 Toeplitz and Circulant Matrices: A review by R.M.Gray. 98 pages.
See more details or get the original Journal article or a printed version.
 Toposes, Triples and Theories by Michael Barr and Charles Wells.
 Trigonometric Delights by Eli Maor. Available also in printed version.
 Understanding Calculus by F.Hussain. Very good.
 Vector Bundles and KTheory by Allen Hatcher.
 Wavelets  all there is to know about them. Do not miss this resource!
 Wolfram MathWorld. The web's most extensive mathematics resource.
Free, online books RELATED to MATHEMATICS
Free, online Math Courses, Lecture Notes and Textbooks
 A Concise Course in Algebraic Topology by J.Peter May. Available also in dvi and print.
 A First Course in Linear Algebra (FCLA), a textbook by Rob Beezer. Excellent.
 A Primer of Real Analysis, an online textbook by Dan Sloughter.
 A Problem Text in Advanced Calculus by John M.Erdman.
 A Short Course in Discrete Mathematics by Edward A. Bender and Gill S. Williamson.
 Abstract Algebra: The Basic Graduate Year, a textbook by Robert B.Ash.
 Abstract Algebra: Theory and Applications, 2009 college textbook by Thomas W.Judson.
 Algebraic Number Theory, a course by Robert B. Ash.
 An Introduction to Set Theory, an almost complete course/textbook
by William Weiss. PDF / PS / DVI formats.
 Analysis of Functions of a Single Variable, a textbook by Lawrence Baggett.
 Basic Analysis: Introduction to Real Analysis, a nice textbook by Jiri Lebl.
 Calculus, a textbook by B.Crowell.
 Calculus, a textbook by Gilbert Strang at MIT Open Courseware.
 Commutative Algebra, a course by Robert B. Ash.
 Complex Analysis interactive textbook by Bert G.Wachsmuth.
 Elementary Linear Algebra, lecture Notes by Keith Matthews.
 Functional Analysis, an online textbook by Lawrence Baggett.
 Fundamentals of Model Theory, a course/textbook
by William Weiss and Cherie D'Mello. PS / DVI / AtlasImage formats.
 Group Theory course by James S.Milne.
 HyperStat Online Statistics Textbook by David M.Lane. Great resource.
 Lectures on Statistics by Robert B. Ash.
 Lectures Notes on Optimization by Pravin Varaiya.
Online PDF reissue of a book out of print since 1975.
 Lectures on Analytic Differential Equations
by Yulij Ilyashenko and Sergei Yakovenko.
Available also in printed form.
 Math Alive, lecture Units by Ingrid Daubechies and Shannon Hughes.
 Modern Course on Curves and Surfaces, lecture notes by R.Palais.
 Notes on Differential Equations, lecture notes by Bob Terrell.
 Notes on Diffy QS: Differential Equations for Engineers, a nice textbook by Jiri Lebl.
 Ordinary Differential Equations and Dynamical Systems, a textbook by Gerald Teschl.
 Real Analysis interactive textbook by Bert G.Wachsmuth.
 Topology Course Lecture Notes by Aisling McCluskey and Brian McMaster.
 Yet Another Calculus Text: A short introduction with infinitesimals,
a textbook by Dan Sloughter.
Free, online MATHEMATICAL THESES


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