Borel Games are multiplayer games with infinite horizon and general payoff functions. These types of games, first introduced by Gale and Stewart (1953), were studied within descriptive set theory in the context of two-player zero-sum games. Only recently have they attracted attention from the broader game theory community. This book is the first attempt to present a comprehensive exploration of Borel Games in a single volume. The book can be used as a main text for a graduate-level course on Borel Games, or as a supplementary text for a more general course on game theory. Students are assumed to be familiar with set theory and to have a basic understanding of general game theory. Features · Replete with exercises, with solutions available online for course instructors · Includes a selection of open problems to invite further study · The first comprehensive coverage of Borel Games in a single volume.