The Archaeology of Knowledge by Michel Foucault is a book that presents a number of challenges. Most obviously, it introduces a lot of new terminology and makes many methodological distinctions, and for this reason presents a certain technical difficulty. However, there are other reasons. First and foremost, it addresses a specific problem that is not really explained in the book itself, concerning how thought in late modernity has responded to the impasse that Foucault describes in the final chapters of The Order of Things, and which hinges on the finitude of man. My first aim in this book is to show that The Archaeology of Knowledge is a deliberate attempt to accelerate a response that was in his view already underway. In addition, Foucault's text does little to make it clear where the most important precedents lie for the conceptual and methodological steps that he takes. For many readers, this is made worse by the fact that some of these precedents may be relatively unfamiliar today. Without some appreciation of them, however, I believe one's understanding of what Foucault is doing in this book will be incomplete. The precedents lie primarily in the philosophy of mathematics, the philosophy of science and the epistemology of the first half of the twentieth century, and in particular in the work of Gaston Bachelard and Jean Cavaillès. Michel Serres' early work on the history and epistemology of mathematics is also very significant, as are other elements of his thinking, such as his readings of atomism and of Leibniz.