Matching Theory (North-Holland Mathematics Studies 121)
L. Lovasz, M. D. Plummer
The subject has obviously advanced a lot since the book was published, but the overview provided is still unmatched. The book has concise and clear expositions of things I did not expect to see there (for example, Kasteleyn's enumeration theory for planar graphs), and which are hard to find anywhere else. Should be right next to Combinatorial Problems and Exercises (AMS Chelsea Publishing) on your bookshelf.
