Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

'... contains so much useful information ... I am sure that the book will fulfil its author's intention and serve as a catalyst for the further development of this fascinating and fertile mathematical field.' J. A. G. Vickers, Bulletin of the London Mathematical Society
'... there is no room for doubt about the author's authority in the subject. As a definitive work at its price every mathematics research library should have a copy.' J. F. Toland, Proceedings of the Edinburgh Mathematical Society
'The book should be warmly recommended to graduate students of mathematics and mathematical physics.' European Mathematical Society Newsletter