Reviewer Darren Glass writes that different parts of the book are aimed at different audiences, resulting in "a wonderful book which can be appreciated on many levels" and providing an unusual level of depth for a popular mathematics book. Its first section, on symmetries of low-dimensional Euclidean spaces, is suitable for a general audience. The second part involves some understanding of group theory, as would be expected of undergraduate mathematics students, and some additional familiarity with abstract algebra towards its end. And the third part, more technical, is primarily aimed at researchers in these topics, although much still remains accessible at the undergraduate level. It also has exercises making it useful as a textbook, and its heavy use of color illustration would make it suitable as a coffee table book. However, reviewer Robert Moyer finds fault with its choice to include material at significantly different levels of difficulty, writing that for most of its audience, too much of the book will be unreadable.