I will be keeping links to legally free textbooks here. If you have any recommendations of repositories or books that I should include, please let me know.
University of Minnesota's Open Textbook Library
The Ohio State University's Ximera Project
American Institute of Mathematics Open Textbook Initiative is a searchable database of “books that are suitable for use in traditional university courses.”
I do not list all the different licences here, but each pdf should include its own open license in the text.
The books listed here are far from a complete list, but are all books that I personally have used or considered using in teaching or research.
The books by Anthony W. Knapp are also available on his website, along with a brief history of the books and how they came to be freely available.
The book by Herbert S. Wilf is also available on his website.
Jim Hefferon's book is also available with more content (slides, labs, etc.) on his website.
Dave Witte Morris has his free books on his website, they are included individually below as well.
Allen Hatcher's website has statements about the copyrights and more information about his books. I include some of them below.
Algebra by Frederick M. Goodman
Basic Algebra by Anthony W. Knapp
Advanced Algebra by Anthony W. Knapp
Introduction to Arithmetic Groups by Dave Witte Morris
Abstract Algebra Theory and Applications by Thomas W. Judson
Generatingfunctionology by Herbert S. Wilf
Enumerative Combinatorics Volume 1 by R.P. Stanley is available for personal use from his website
Dartmouth has an entire course called the Chance course. There you can find a textbook (also linked to here: Introduction to Probability by Charles M. Grinstead and J. Laurie Snell), web applications, and teacher's guide.
Ratner's Theorems on Unipotent Flows by Dave Witte Morris
Ergodic Theory, Groups, and Geometry by Robert J. Zimmer and Dave Witte Morris
Proofs and Concepts by Dave Witte Morris and Joy Morris
Book of Proof by Richard Hammack
Linear Algebra by Jim Hefferon
Linear Algebra Done Wrong by Sergei Treil. The copyright and more information is on Sergei Treil's homepage.
Linear Algebra via Exterior Products by Sergei Winitzki
Basic Real Analysis by Anthony W. Knapp
Advanced Real Analysis by Anthony W. Knapp
Real Analysis for Graduate Students by Richard F. Bass. Here is a link to his website with errata.
A First Course in Complex Analysis by Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka
Algebraic Topology by Allen HatcherLast Updated October 29, 2016