Detailed and clear, yet focused on the essentials, the book introduces graph theory. For each topic, the author presents the fundamentals and then proves typical theorems, often supplemented by a discussion of their underlying ideas. In this way, he exemplifies the most important methods of contemporary graph theory, including modern techniques such as the Regularity Lemma, random graphs, tree decompositions, and minors. The 4th updated and expanded edition includes complete solution hints for all exercises.