we followed Huffman-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.