A lot of math majors, and a few non-math majors, take a "transitions" course just after taking their multivariable calculus course to prepare for RIGOROUS treatment of linear algebra, real analysis, abstract algebra, and other higher math topics. You can find many textbooks for those subjects by browsing around Amazon.com (which is how I've discovered most of them over the years) and one list of those books
http://www.amazon.com/exec/obidos/tg.../31B4QV24TPSZ/
will lead you to other books of the same kind, so you can see what is appealing to you for self-study.