The topic here is not to harmonize theories, but theory about how to match things--usually members of one group with members of another. Award-winning Hungarian mathematician Lovász (Eötvös Loránd U., Budapest) and fellow specialist in combinatorics Plummer (mathematics, Vanderbilt U.) discuss matchings in bipartite graphs, network flow theory, the size and structure of maximum matchings, bipartite graphs with perfect matching, some graph theory problems related to matching, matching and linear programming, determinants and matching, matching algorithms, the f-factor problem, matroid matching, and vertex packing and covering. A new appendix reviews the incident of the Markov Chain Monte Carlo method and other adventures of the theory and its applications since the book's original publication in 1986 by North Holland Publishing Company, Amsterdam and Akadémiai Kiadó in Budapest. A Russian edition was published in 1999. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)