Here is a lucid introduction to the ideas of symmetry as they are so successfully used in the fields of physics, chemistry and other physical sciences.  Using only elementary mathematics, the author discusses the subtle relationship between physical objects, models, and icons, and explains some of the so-called symmetry paradoxes.  Each of the three chapters uses a case-study to illustrate the development of major concepts.  In the first two chapters, the focus is on the concept and importance of an icon.  The author explains the origins and applications of symmetry, and shows how rotations came to be described by Hamilton by means of quaternions.  This approach gives insight into the symmetry properties of vectors and demonstrates the relevance of tensors and spinors.  The third chapter illustrates the use of symmetry in the classification of energy levels in atoms and solids, and discusses broken symmetry.  With its use of simple, easy-to-understand mathematics, the book will appeal to a wide range of readers interested in the philosophy and history of science, science in general, and physics specifically.  It may also serve as useful supplementary reading for students in these fields.

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