Without getting bewildered I would suggested going through these 3:

1. Book of Proof by Hammack (http://www.people.vcu.edu/~rhammack/BookOfProof/)

2. Calculus by Spivak

3. Linear Algebra Done Right by Axler

Be prepared to work through all (or at the very least only the odd numbered) exercises. If you can't stomach that or find that life gets in the way of you completing even these very basic books, you do not have the time or discipline required to advance in mathematics.