Benson Farb and Dan Margalit have just finished the final version of A Primer on Mapping Class Groups, to appear from Princeton University Press next year. And it’s available in .pdf at Dan’s web page. To the extent I know anything about mapping class groups, it’s because of this book! Highly recommended for anyone interested in finding a way into this very active area of topology, which has heretofore not been so easy to learn about unless you have the luck to sit at the feet of a master. Is it too much to say I expect the book to become “the Hartshorne of the mapping class group?”
I can also recommend “Problems on mapping class groups and related topics”, Proc. Symp. Pure Math. 74, A.M.S (2006), edited by B. Farb, and the survey of N. Ivanov, in the “Handbook of geometric topology”…
It’s finished just in time for my topics course in the Fall!