And some introductory mathematical logic.
From this you can immediately move to Analysis on the real line (up to Reimann integrals)
Linear Algebra is also something you can start (Kenneth Hoffman and Ray Kunze https://www.amazon.com/Linear-Algebra-Kunze-Hoffman/dp/93325...)
Once you are comfortable with Riemann Integrals, you can start attacking Complex Variables (John Conway has excellent springer texts: Functions of One Complex Variable Vol 1 and 2)
Some texts you should look at after you understand basic set theory:
1. [Michael_Spivak]_Calculus - good book for introduction to real analysis
2. [johnsonbaugh,pfaffenberger]_Foundations_of_Mathematical_Analysis - Dover publications
3. [Vladimir_A._Zorich]_Mathematical_Analysis_I - well written but less known. Recommend checking it out.
4. [Gerald_B._Folland]_Real_Analysis_Modern_techniques_and_their_applications - My top pick, but a tough read.
5. [Rudin_Walter]_Principles_of_Mathematical_Analysis - classic book
1. [David_Lay]_Linear_Algebra_and_Its_Applications -
2. [Friedberg,Insel,Spence]_Linear_algebra - Undergraduate level text
3. [Hoffman,Kunze]_Linear_Algebra_2nd_edition - Graduate level text. My top pick.
4. [Gilbert_Strang]_Introduction_to_Linear_Algebra - Undergraduate level linear algebra. Same guy has MIT OCW lectures.
Complex Variables/Complex Analysis:
1. [John_Conway]_Functions_of_One_Complex_Variable_I - My top pick
2. [Lars_Ahlfors]_Complex_Analysis_(Third_Edition) - Classic. Not a big fan though.