[laichzeit0]

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.

[aoki]

might be worth noting that "calculus by spivak" is famously mistitled and is what people today call an intro analysis text. (says so right in the intro :-)

there are now "warm up" books (alcock) as well as even more basic real analysis books (abbott, about half the length of spivak).

[1457389]

Thank you!

[sn9]

If you make it through all of those, pick up Hubbard and Hubbard's Vector Calculus for a unified treatment of multivariable calculus and linear algebra.