This comprehensive textbook on combinatorial optimization places special�emphasis on theoretical results and algorithms with provably good�performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout,�it contains complete but concise proofs, and also provides numerous�exercises and references. This fifth edition has again been updated, revised, and significantly�extended, with more than 60 new exercises and new material on various�topics, including Cayley's formula, blocking flows, faster�b-matching separation, multidimensional knapsack, multicommodity�max-flow min-cut ratio, and sparsest cut. Thus, this book represents the state of the art of combinatorial optimization.