When it comes to self-studying proof-based math, a few classic books are highly recommended. "How to Prove It" by Daniel J. Velleman is an excellent choice for beginners. For a deeper dive, "Principles of Mathematical Analysis" by Walter Rudin is a classic for real analysis. "Introduction to the Theory of Sets" by Joseph Breuer is great for set theory. Don't forget to complement your studies with online resources, like lecture notes and problem sets from universities.