This book now appears in a fourth edition, which includes a Bibliographical Supplement that continues the previous ones up to 2015. It proposes an interpretation of the Timaeus that takes into account all those that have been proposed throughout the ages. In the Timaeus, Plato undertakes a twofold task. On the one hand, he conforms to tradition by telling the tale of the world's origin after the manner of Hesiod; while on the other, he appears as a predecessor of Galileo, by proposing a cosmological model based on mathematics. In both cases, he shows originality. His story is no longer based on the sexual union that ensures the succession of divine royalties, but on the work of a craftsman and an artist. To describe the world that surrounds us, moreover, Plato no longer uses ordinary language as Aristotle was also to do, but the most recent developments of mathematics of his time. This book is intended as a systematic commentary on Plato's Timaeus. One chapter is devoted to each of the following themes: the demiurge, the intelligible forms, the spatial environment, the world soul, the world's body, man, and necessity. On each of these themes, extensive account of the many interpretations proposed in Antiquity: those of the Old Academy, of Middle Platonism, and of Neoplatonism. These interpretations, which succeed one another as a function of diverse concerns, are multiple, but not infinite; what is more, they are taken up, explicitly or not; by modern interpretations.