Symmetry is one of the ideas by which man through the ages has tried to comprehend and create order, beauty, and perfection. Starting from the somewhat vague notion of symmetry = harmony of proportions, this book gradually develops first the geometric concept of symmetry in its several forms as bilateral, translator^, rotational, ornamental and crystallographic symmetry, and finally rises to the general abstract mathematical idea underlying all these special forms.

Professor Weyl on the one hand displays the great variety of applications of the principle of symmetry in the arts, in inorganic and organic nature, and on the other hand he clarifies step by step the philosophical- mathematical significance of the idea of symmetry. The latter purpose makes it necessary for the reader to confront the notions and theories of symmetry and relativity, while a wealth of illustrations sup- porting the text help to accomplish the former.

This book is semi-popular in character. It does not shun mathematics, but detailed treatment of most of the problems it deals with is beyond its scope.

The late Professor Weyl was world famous for his contributions to mathematics and the philosophy of science. In this book his penetrating mathematical insight illumines and transforms the worlds of nature and of art.