Basic Graph Theory -- Algorithms and Complexity -- Shortest Paths -- Spanning Trees -- The Greedy Algorithm -- Flows -- Combinatorial Applications -- Connectivity and Depth First Search -- Colorings -- Circulations -- The Network Simplex Algorithm -- Synthesis of Networks -- Matchings -- Weighted matchings -- A Hard Problem: The TSP.From the reviews of the first edition: ".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..." Mathematical Reviews 2002 This thoroughly revised new edition offers a new chapter on the network simplex algorithm and a section on the five color theorem. Moreover, numerous smaller changes and corrections have been made and several recent developments have been discussed and referenced.