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ONAG, as the book is known, is one of those rare publications that sprang to life in a moment of creative energy and has remained influential for over a quarter of a century. Still in high demand, it is being republished with some adjustments and corrections. The original motivation for writing the book was an attempt to understand the relation between the theories of transfinite numbers and mathematical games. By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers (so named by Donald Knuth) that includes at the same time the real numbers and the ordinal numbers.

This new edition ends with an epilogue that sets the stage for further research on surreal numbers. The book is a must-have for all readers with a serious interest in the mathematical foundations of game strategies.