Substantially revised reorganised and updated the second edition now comprises eighteen chapters carefully arranged in a straightforward and logical manner with many new results and open problems. As well as covering the theoretical aspects of the subject with detailed proofs of many important results the authors present a number of algorithms and whole chapters are devoted to topics such as branchings feedback arc and vertex sets connectivity augmentations sparse subdigraphs with prescribed connectivity and also packing covering and decompositions of digraphs. Throughout the book there is a strong focus on applications which include quantum mechanics bioinformatics embedded computing and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation and more than 650 exercises 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject.