Looking for a 'second course' in logic and set theory (forcing, large cardinals...) I'm a recent graduate and will likely be out of the maths business for now - but there are a few things that I'd still really like to learn about - forcing and large cardinals being two of them.
My background is what one would probably call a 'first graduate course' in logic and set theory (some intro to ZFC, ordinals, cardinals, and computability theory). Can you recommend any books or online lecture notes which are accessible to someone with my previous knowledge?
Thanks a lot!
 A: Kunen's "Set Theory: An Introduction to Independence Proofs" is a really well written introduction to, well, independence proofs.  It doesn't do a lot with large cardinals, at least not the really large ones, but it does do a thorough treatment of forcing.  It also develops Godel's constructible universe in proving the consistency of AC and GCH with ZF, along with other basic methods used in proofs of independence or consistency.  I think it finds a good balance between being a gentle introduction, but also efficiently getting through the material.  I would highly recommend it for a second set theory course.
A: I would recommend the following as excellent graduate level introductions to set theory, including forcing and large cardinals. 


*

*Thomas Jech, Set Theory. 

*Aki Kanamori, The higher infinite.  See the review I wrote of it for Studia Logica. 
I typically recommend to my graduate students, who often focus on both forcing and large cardinals, that they should read both Jech and Kunen (mentioned in Francis Adams answer) and play these two books off against one another. For numerous topics, Jech will have a high-level explanation that is informative when trying to understand the underlying idea, and Kunen will have a greater level of notational detail that helps one understand the particulars. Meanwhile, Kanamori's book is a great exploration of the large cardinal hierarchy. 
I would also recommend posting (and answering) questions on forcing and large cardinals here and also on mathoverflow. Probably most forcing questions belong on mathoverflow.
