There are many books, papers and lecture notes which give an introduction to forcing (e.g. Jech's or Kunen's books) but here I am looking for some possibly less-famous useful comprehensive texts about forcing with a wide range of solved/unsolved problems and a nice description of what is going on in usual, iterated and proper forcings.
Remark: I should emphasize that I am looking for a new (and possibly graphic) intuition about forcing.
Here are two references that are not Kunen/Big Jech.
Jech - Multiple Forcing, it is a small book which covers the basics of forcing, products of forcing, iterated forcing, and proper forcing. All with a few nice uses (e.g. Martin's Axiom and some of its uses).
Halbeisen - Combinatorial Set Theory, a book containing a very nice introduction to set theory. This includes basics of logic, axioms, axiom of choice discussion, models with atoms. And of course, forcing including a lot of the coverage of the basics, and up to intermediate techniques.
Word of caution, Halbeisen uses the Jerusalem convention which forces up, rather than down. This can be confusing if one never saw that before.
You can also find some fragments in Kanamori's The Higher Infinite, but the book has no chapter which is fully dedicated to forcing. Shelah's Proper Forcing as well Proper and Improper Forcing also contain a lot of information on the topic, in the latter book the exposition to forcing was edited (or written? I forget now) by Azriel Levy, which makes it very gentle and understandable. I'm not sure if later parts about iterations have these qualities, I haven't read through them.