Providing a cohesive reference for advanced undergraduates, graduate students and even experienced researchers, this text contains both introductory and advanced material in extremal graph theory, hypergraph theory and Ramsey theory. Along the way, the book includes many modern proof techniques in the field such as the probabilistic method and algebraic methods. Several recent breakthroughs are presented with complete proofs, for example, recent results on the sunflower problem, and off-diagonal and geometric Ramsey theory. It is perhaps unique in containing material on both hypergraph regularity and containers. Featuring an extensive list of exercises, the text is suitable as a teaching text for a variety of courses in extremal combinatorics. Each of the two parts can form the basis of separate courses, and the majority of sections are designed to match the length of a single lecture.

‘A treasure trove of material for teachers of advanced courses on extremal graphs and hypergraphs. The book gives a thoughtfully curated presentation of this vibrant field, from its classical beginnings right through to present-day research developments. It is sure to become an essential resource for students, researchers and educators.'

Penny Haxell - University of Waterloo

‘Extremal Graph and Hypergraph Theory is a vibrant area of modern Discrete Mathematics. Mubayi and Verstraete describe the major themes of the subject, and provide a beautiful presentation of many of the most exciting recent developments. Written by two leading experts, this fascinating text will benefit students and researchers interested in the field and its applications.'

Noga Alon - Princeton University