Online Mathematics Textbooks

Here is a list of online  Mathematics textbooks    available for free downloading in various formats  or for online reading:

1. Linear Methods of Applied Mathematics, by Evans Harrell and James Herod.
2. Linear Algebra, Infinite Dimensions, and Maple, by James Herod.
3. Complex Variables , by Robert Ash and W. P. Novinger. This is a substantial revision of the first edition of Professor Ash’s complex variables text originally published in 1971.
4. Professor E.H. Connell of the University of Miami has made available on the web his book Elements of Abstract and Linear Algebra. You should read his insightful comments about textbooks.
5. An introductory algebraic topology book, Algebraic Topology I, by Professor Allen Hatcher, of Cornell University, is available, and Professor Hatcher promises the second volume, Algebraic Topology II, will be ready soon.
6. The Geometry and Topology of Three-Manifolds, by William Thurston. This is an electronic edition of the 1980 lecture notes distributed by Princeton University.
7. Professor Jim Hefferon of Saint Michaels’s College has made available his undergraduate textbook Linear Algebra.
8. Another elementary linear algebra textbook is Elementary Linear Algebra, by Keith Matthews.
9. Introduction to Probability, by Charles Grinstead & J. Laurie Snell.
10. An Introduction to Probability and Random Processes, by Gian-Carlo Rota and Kenneth Baclawski. This is the 1979 manuscript of the work Professor Rota had been working on for some time. It is made available through the efforts of David Ellerman.
11. Furnished by David Joyce is a version of perhaps the greatest textbook of them all, Euclid’s Elements.
12. Daniel Callahan has also provided what he calls a “an open textbook based on Euclid’s Elements”, Euclid’s ‘Elements’ Redux.
13. Originally published by Springer-Verlag, the book A Course in Universal Algebra, by Stanley Burris, and H. P. Sankappanavar, is available online.
14. Professor Robert Ash has written and made available Abstract Algebra:The Basic Graduate Year.
15. Another one by Professor Ash is A Course In Algebraic Number Theory.
16. Professor Ash has also completed and made available A Course in Commutative Algebra.
17. Understanding Calculus, by Faraz Hussain.
18. Originally published by Prindle, Weber & Schmidt but currently out of print, Elementary Calculus: An Approach Using Infinitesimals, by Professor H. Jerome Keisler, is now freely available online.
19. Graph Theory, by Reinhard Diestel.
20. Available for self-study from The Trillia Group is Basic Concepts of Mathematics, by Elias Zakon.
21. Another one from The Trillia Group is An Introduction to the Theory of Numbers by Leo Moser.
22. Also from The Trillia Group are Mathematical Analysis I, and Mathematical Analysis II, by Elias Zakon.
23. Thanks to Malaspina Great Books, Mechanism of the Heavens (1831), by Mary Somerville, is available online. This second edition was prepared by Russell McNeil.
24. Lecture Notes on Optimization, by Pravin Varaiya. This is a re-issue of a book out of print since 1975. It is an introduction to mathematical programming, optimal control, and dynamic programming.
25. Published by Cambridge Press, but still freely available is Mathematical Ilustrations, by Bill Casselman.
26. A Problem Course in Mathematical Logic, by Stefan Bilaniuk .
27. Concepts and Applications of Inferential Statistics, by Richard Lowry.
28. Published by Cambridge University Press, A Computational Introduction to Number Theory and Algebra, by Victor Shoup is nevertheless freely available on-line. 
29. Designed for undergraduate physics students is Mathematical Tools for Physics, by James Nearing.
30. A First Course in Linear Algebra, by Rob Beezer.
31. Group Theory, by Pedrag Civitanovic.
32. Shlomo Sternberg has written Theory of Functions of a Real Variable.
33. Lie Algebras is another one by Professor Sternberg
34. Yet another one by Professor Sternberg is Semi-Riemann Geometry and General Relativity
35. Advanced Calculus, by Lynn Loomis and Schlomo Sternberg
36. Difference Equations to Differential Equations, by Dan Sloughter.
37. The Calculus of Functions of Several Variables is another one by Professor Sloughter.
38. Notes on Differential Equations, by Bob Terrell.
39. Sets, Relations, Functions, by Ivo Düntsch and Günther Gediga.
40. Another one by Düntsch and Gediga is Rough Set Data Analysis.
41. Predicative Arithmetic, by Edward Nelson.
42. Toposes, Triples and Theories, by Michael Barr and Charles Wells. This was orinally published by Springer-Verlag, 1985
43. Information Theory, Inference, and Learning Algorithms, by David J. C. MacKay is published by Cambridge University Press, but is, nevertheless, freely available online.
44. Numerical Methods and Analysis for Engineers, by Douglas Wilhelm Harder.
45. Analysis of Functions of a Single Variable, by Lawerence Baggett, was originally written to be used for a one semester senior course, but the author suggests that it is more appropriate for first year graduate students.
46. Convex Optimization, by Stephen Boyd, and Lieven Vandenberghe is freely available thanks to Cambridge University Press.
47. Introduction to Statistical Signal Processing, by R. M. Gray and L. D. Davisson is, according to Professor Gray, a “…much revised version of the earlier textRandom Processes: An Introduction for Engineers, Prentice-Hall, 1986, which is long out of print.” The current book is published by Cambridge University Press.
48. Abelian Categories, by Peter Freyd. This was published originally by Harper & Row.
49. Published by Van Nostrand in 1971 and now available is Categories and Groupoids, by P. J. Higgins.
50. Basic Concepts of Enriched Category Theory, by G. M. Kelley, was published by Cambridge University Press.
51. Abstract and Concrete Categories:The Joy of Cats, by Jiri Adamek, Horst Herrlich, and George Strecker.
52. Abstract Algebra:Theory and Applications, by Tom Judson.
53. Originally published by Pearson in 2003, Introduction to Real Analysis, by William F. Trench is now freely available.
54. Another by Professor Trench is Elementary Differential Equations, originally published by Brooks/Cole Thompson Learning.
55. Elementary Differential Equations With BoundaryValue Problems, also by Professor Trench, and also originally published by Brooks/Cole Thomson Learning.
56. Notes on Diffy Qs: Differential Equations for Engineers, by Jiří Lebl .
57. According to the authors, Proofs and Concepts: the fundamentals of abstract mathematics, by Dave Morris, and Joy Morris, provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics.
58. Mathematical Biology, by Jeffrey Chasnov.
59. Originally published in 1970, Calculus and Linear Algebra. Vol. 1 and also Calculus and Linear Algebra. Vol. 2, by Wilfred Kaplan and Donald J. Lewis, are available thanks to the Scholarly Publishing Office of the University Library at University of Michigan.
60. Lectures on Probability, Statistics and Econometrics, by Marco Taboga.
61. Introduction to Calculus I and II, by J.H. Heinbockel.
62. Active Calculus, by Matt Boelkins.
63. Analytic Combinatorics, by Philippe Flajolet and Robert Sedgewick.
64. Mathematical Reasoning: Writing and Proof, by Ted Sundstrom. Earlier editions of this one were published by Pearson Education, Inc., but this most recent edition is now freely available.
65. Linear Algebra, by David Cherney, Tom Denton, and Andrew Waldron