Self-similarity is a profound concept that shapes many of the laws governing nature and underlying human thought. It is a property of widespread scientific importance and is at the centre of much of the recent work in chaos, fractals, and other areas of current research and popular interest. Self-similarity is related to svmmetry and is an attribute of many physical laws: particle physics and those governing Newton's laws 0 , gravitation. Symmetry, found throughout the biological universe, is also a basic property of the mathematical universe. In this book the author explores the ideas of scaling, self-similarity, chaos and fractals as they appear throughout the universe of pure and applied mathematics. Because of his formidable research experience, stretching from the acoustical modelling of concert halls to pure number theory, Schroeder is able to take the reader on an intellectual excursion through this vast forest of topics.