The book is a history of symmetry and group theory, and their application to physics. The format, after a rough start in Babylonia and ancient Greece, consists mainly of biographical sketches followed by a high-level explanation of a mathematical advance. This mix didn't work particularly well for me because the Nth mathematician to study at European universities, get married, and have children is pretty much like the N-1th. Except for the ones that die young like Galois and Abel.
The chapter on Galois is the best of the lot. The explanation of Galois' work is detailed enough to provide some understanding of the result, without getting overly technical. Unfortunately, this was the part of the history I was most familiar with. (The Galois theory text I own is not Stewart's, though.) The treatment of quaternions is interesting as well, but most of the other topics are dealt with only superficially. The book is an OK overview with interesting tidbits; there is certainly enough to spark interest in the topics covered.
The penultimate chapter on the relationship between octonions (8-dimensional numbers) and the exceptional simple Lie groups was particularly interesting, but again I felt that the text could have gone a level deeper without losing too many readers. The final chapter is a mini-essay on the link between mathematical beauty and physical truth. There are some interesting ideas here but they deserve to be explored in more depth. I felt that the biographical and mathematical developments really didn't succeed in leading me to the point where that chapter was sufficient.