This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. It contains complete but concise proofs, also for many deep results, some of which did not appear in a textbook before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. This fourth edition is again significantly extended, most notably with new material on linear programming, the network simplex algorithm, and the max-cut problem. Many further additions and updates are included as well. From the reviews of the previous editions: "This book on combinatorial optimization is a beautiful example of the ideal textbook." Operations Research Letters 33 (2005), p.216-217 "The second edition (with corrections and many updates) of this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization." OR News 19 (2003), p.42 "... has become a standard textbook in the field." Zentralblatt MATH 1099.90054.