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.