TITLE: What are some good books about martingales?
QUESTION [7 upvotes]: I'm looking for suggestions for well written books dealing with martingale theory, not necessarily exclusively. I'm also looking for a nice compilation of problems, preferably with answers, on this topic.
EDIT: I'm particularly interested in discrete time martingales.

REPLY [5 votes]: René Schilling: Measures, Integrals and Martingales 
The solution manual is not contained in the book, but available on the web page.