This book is a concise — yet most carefully written — introduction tomodern graph theory, covering all its major recent developments. It canbe used both as a reliable textbook for an introductory course and asa graduate text: on each topic it covers all the basic material infull detail, and adds one or two deeper results (again withdetailed proofs) to illustrate the more advanced methods of that field. This second edition extends the first in two ways. It offers athoroughly revised and updated chapter on graph minors, which nowincludes full new proofs of two of the central Robertson-Seymourtheorems (as well as a detailed sketch of the entire proof of theircelebrated Graph Minor Theorem). Secondly, there is now a section ofhints for all the exercises, to enhance their value for both individual study and classroom use.