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The two editions of our book Digraphs: Theory, Algorithms and Applications, which were published by Springer in 2000 and 2009, respectively, remain the only modern books on graph theory covering more than a small fraction of the theory of directed graphs. We are happy to see that the book has been useful, both for students of advanced courses and to researchers from a wide range of areas, some of which are far from mathematics, such as sociology and medicine. Since we completed the second edition in 2008, the theory of directed graphs has continued to evolve at a high speed; many important results, including solutions some of the conjectures from Digraphs, have appeared and new methods have been developed. So we were faced with the choice of either writing a 3rd edition of our book or developing a new book from scratch. We decided to do the latter for the following main reason: By taking a new …