There have been many advances?in graph edge coloring since the 1990s, and this book provides an overview of this development as well as?describes how the many different results are related.??Many new improved proofs of known results are featured,? important unsolved problems are identified, and new results and connections?are described.? Most prominently, a very important step forward is the theory of Tashkinov, which?at the moment is only?available in Russian. ?Tashkinov has collobarted with the authors to provide?a comprehensive, new, and accessible version of Tashkinovs theory and results. The method of Taskinov is used to give an asymptotic positive solution to Goldbergs conjecture.? Chapter coverage includes an introduction to coloring preliminaries and lower and upper bounds; the Vizing fan; the Kierstead path; simple graphs and line graphs of multigraphs; the Tashkinov tree; Goldberg's conjecture; extreme graphs; generalized edge coloring; and open problems.