TITLE: Books on logic, proof theory and set theory?
QUESTION [12 upvotes]: I graduated in Computer Science at University of Bologna in Italy some years ago.
For various reasons now I am discovering a back interest in mathematic logic higher than I was a student.
I have only a pair of university books about the subject. Now I am reading that books and I am enhancing the not so developed concepts using mainly Wikipedia.
Because of this reason, maybe what I am going to write consecutively is a bit confused.
Now I am looking for the minimal list of books that cover the following areas:

All kinds of logic: classical, intuitionstic, relevance, etc...
Proof theory
Set theory
Philosophical implications

For each of these areas I am interested its history too.
Every help is really appreciated.

REPLY [3 votes]: You might find Graham Priest's An Introduction to Non-Classical Logic interesting. It certainly covers the non-classical logics that interest you, with some brief, but useful historical notes, and discussion of the philosophical implications by one of the leading contemporary philosophical logicians.