Du Sautoy specializes in symmetry, and that concept is instantly visualized in the tiling of the Moorish Alhambra Palace, which initiates his tour through the history and ideas of his mathematical subject. This accessible introduction makes for a shrewd start, for, as seems congenital with mathematicians and their abstract pursuits, du Sautoy takes symmetry in this work to the nth degree—specifically, to the 196,883d dimension. But far from stumping his readers, the author inveigles them with clarity about symmetry’s foundational concepts, cast of mathematical heroes, and wry portrayals of the quirky personalities among his contemporary colleagues in group theory, as symmetry is technically called. The package works as well here as in his highly praised The Music of the Primes (2003), with the addition of imparting the personal frisson of making a mathematical discovery. Relating his triumphs, confiding his worry about whether, at age 40, he’s still got the creative spark, du Sautoy well demonstrates that whatever discoveries he has yet to make, he’s able to engage general readers in the cerebral dramas of pure mathematics.