Book recommendation about set theory and mathematical logic

Question

I finished some elementary proof-writing courses, but I am not quite familiar with mathematical logic and set theory yet. Can you recommend some books that cover set theory and mathematical logic in one book?

Your recommendations about books on set theory or mathematical logic alone will be appreciated, though.

Answer 1

The Open Logic Project has some books on logic and set theory. They're all free and open source.

There are also some questions on the site that cover half your question.

For example, this decade-old question lists books on mathematical logic, but doesn't say which ones also cover set theory.

Answer 2

For an extensive guide, with book recommendations at various levels, see the freely downloadable Beginning Mathematical Logic: A Study Guide