STARTING from the somewhat vague notion of symmetry = harmony of proportions, these four lectures gradually develop first the geometric concept of symmetry in its several forms, as bilateral, translatory, rotational, ornamental and crystallographic symmetry, etc., and finally rise to the general idea underlying all these special forms, namely that of invariance of a configuration of elements under a group of automorphic transformations. I aim at two things: on the one hand to display the great variety of applications of the principle of sYl.l1metry in the arts, in inorganic and organic nature, on the other hand to clarify step by step the philosophicomathematical significance of the idea of symmetry. The latter purpose makes it necessary to confront the notions and theories of symmetry and relativity, while numerous illustrations supporting the text help to accomplish the former.
As readers of this book I had a wider circle in mind than that of learned specialists. It does not shun mathematics (that would defeat its purpose), but detailed treatment of most of the problems it deals with, in particular complete mathematical treatment, is beyond its scope. To the lectures, which reproduce in slightly modified version the Louis Clark Vanuxem Lectures given by the author at Princeton University in February 1951, two appendices containing mathematical proofs have been added.
