A Course in Enumeration (Graduate Texts in Mathematics, 238)

Enumerative combinatorics often gets the handbook or encyclopedia treatment owing to the enormous breadth and discontinuity of the subject and the seeming infinite binomial identities that doge the subject. Such variety, much complication. On the flip side, you might find a tome based on a pet-species-framework that tries to be the one finite ring to rule them all, and haz a cheezburger at the same time. Lucky for us, we have a happy medium right here in this book. It's well-organized and cohesively laid out. The author addresses the issues of mixed-bag wikinomics vs. exposition from the start, taking his cue from John Riordan's earlier attempts at unification of identities. Concrete in focus (as enumeration should be), the author stays away from name dropping in the Grand Eponymous Taxonomy game of inter-disciplinary authorial backscratching. Nor is it heavily weighted toward "word" trends in combinatorics, or even the analytic generating function aspects (both are still discussed in limited form). You've probably have your own sources for that, and the book is thick enough already. It has a weakness to my mind, it's a lack of "open problems" and relatedness to open problems recently solved or otherwise.