The modern term ‘symmetry’ brings together a variety of disparate and over-lapping notions, some of which fall under the modern group-theoretic definition now used in mathematical science. The rise of symmetry considerations to dominance in contemporary fundamental physics occurred in the twentieth century, and the modern group-theoretic concept has been explored by philosophers of physics in recent decades. Our scientific concepts are hard-won, forged in the heat of theoretical and practical utility: historical studies displaying some of the ways in which important scientific concepts were formed—and continue to develop—are very welcome. Hon and Goldstein’s book is, primarily, a historical study of the term ‘symmetry’ and the concepts associated with it up to the early 1800s. They are interested in what becomes of the Greek terms ‘summetria’ and ‘summetros’, and the concepts associated with them. Their historical narrative has two aspects: the first traces the use of the term ‘symmetry’, while the second looks for evidence of features of the modern concept of reflection symmetry independent of terminology. The historical narrative contains two trajectories, which Hon and Goldstein label ‘mathematical’ and ‘aesthetic’. In mathematics, ‘symmetry’ was used to mean ‘having a common measure’, while aesthetically it meant well-proportioned. These ‘two trajectories’ should not be thought of as capturing a clean separation. The mathematical trajectory is covered in Chapter 2, beginning with Euclid’s Elements. Hon and Goldstein locate the ‘common measure’ concept attaching to the term ‘symmetry’ also in Archimedes (in mathematical contexts, and in mechanics with respect to the balance and equilibrium). Commensurability was an issue in astronomy. Thus, Hon and Goldstein quote from Oresme’s discussion of whether the motions of the heavens are commensurable: do the periods of the planets have a common measure?