A few links
I stumbled across a few interesting free books in the last few days.
1. Tony Roy has a 1051 page introduction to logic on his homepage, which slowly and evenly proceeds from formalising ordinary-language arguments all the way to proving Gödel's second incompleteness theorem. All entirely mainstream and classical, but it looks nicely presented, with lots of exercises.
2. Ariel Rubinstein has made his six books available online (in exchange for some personal information): Bargaining and Markets, A Course in Game Theory, Modeling Bounded Rationality, Lecture Notes in Microeconomics, Economic Fables, and the intriguing Economics and Language, which applies tools from economics to the study of meaning.
3. Brendan Fong and David Spivak wrote a free textbook on applied category theory. I've dabbled in category theory every now and then (e.g. when trying to work through some of Silvio Ghilardi's work on counterpart semantics), but I never really got the hang of "why?". Peter Smith's (also free) Gentle Introduction to Category Theory helped a little, but Fong and Spivak approach the question much more directly. John Baez is currently going through the book in an "online course", giving his own commentary and exercises on each chapter. (Well, on chapter 1, so far.)