Hermann Weyl's book on symmetry is a good companion to John Conway's recent book on same subject with the title The Symmetries of Things. Conway has more details and more pictures, but Weyl gives a better verbal description of the basic ideas involved, especially the philosophical concepts.

From Weyl we get the idea of the analogy between Galois theory and relativity theory based on their reliance on symmetry expressed by groups and invariants (p. 138 in my 2009 reprint). Another gem is the assertion that all a priori results in physics are due to symmetry (p.126). A rather controversial concept is that objectivity (reality?) relies on invariance (p. 132) and hence symmetry..

On a different level, this book has a good discussion of the relations between the various planar and spatial symmetries such as the space groups and the point (lattice) groups of crystal structure. Numerous minor facts (such as the constructability of a 17 sided regular polygon with ruler and compass) salt the main flow of deep philosophical nourishment. ( )