This book reconstructs key aspects of the early career of Descartes from 1618 to 1633; that is, up through the point of his composing his first system of natural philosophy, Le Monde in 1629-33. It focusus upon the overlapping and intertwined development of Descartes projects in physico-mathematics, analytical mathematics, universal method, and, finally, systematic corpuscular-mechanical natural philosophy. The concern is not simply with the conceptual and technical aspects of these projects; but, with Descartes agendas within them and his construction and presentation of his intellectual identity in relation to them. Hence, the subject matter is selective and ultimately limited in relation to the potential field of concerns in which intellectual historians and historians of science and philosophy might place Descartes, even the young Descartes. It explains, the focus on technical projects, agendas and identity well fits the scope and aim of scientific or intellectual biography. ?