
Needless to say, these books are focussed on High School math but should be sufficient preparation for courses on a more rigorous level.
My email is in my profile if you are looking for somebody to study with.
1. Book of Proof
1a. How to Prove It: A Structured Approach
2. Elements of Set Theory - Enderton
2a. Naive Set Theory - Halmos
3. Foundations of Analysis - Landau
4. Basic Mathematics - Lang
5. Principles of Mathematics - Allendoerfer & Oakley
6. A Transition to Advanced Mathematics
6a. Concept of Modern Mathematics - Stewart
7. Calculus - Apostol or Spivak
Don't skip any