Much of the material in the book is either new, or previously known only through technical publications aimed at specialists, and much of the previously-known material that it presents is described in new notation and nomenclature. Although there are many other books on symmetry, reviewer N. G. Macleod writes that this one "may well become the definitive guide in this area for many years". Jaron Lanier calls it "a plaything, an inexhaustible exercise in brain expansion for the reader, a work of art and a bold statement of what the culture of math can be like", and "a masterpiece".