Recommendations for books on set theory include "Naive Set Theory" by Halmos, which is well-regarded for its clarity. "Axiomatic Set Theory" by Suppes is mentioned, though it has some issues. "Theory of Sets" by Kamke is also suggested. For a more comprehensive approach, "Set Theory" by Hrbacek and Jech is recommended for its depth. If a basic understanding is sufficient, "Book of Proof" by Richard Hammack and "How to Prove It" by Daniel Velleman are good options, with Hammack's book available for free online. However, the preference expressed is for rigorous material, particularly those that include problems to reinforce understanding.