Books on set and proof theory

Question

I have recently been fascinated by theorems and statements in set and proof theory, such as formally demonstrating the independence of propositions (eg, independence of the Continuum Hypothesis from ZFC, independence of AC from standard ZF axioms, etc) and am interested in self-studying these problems in greater depth. I am looking for a book or other source I could learn from, which focuses on nontrivial applications of foundational set theory to problems like those I described above. I am a first year CS undergrad, but have some mathematical maturity and self study experience (I am currently working through Roman's Advanced Linear Algebra). I would prefer if the book focused more on problems and applications (to problems in set theory, of course) rather than developing the theory as fast as possible