This book has a double purpose. First, to trace the historical development of the concepts of the continuous and the infinitesimal; and second, to describe the ways in which these two concepts are treated in contemporary mathematics. So the first part of the book is largely philsophical, while the second is almost exclusively mathematical. In writing the book I have found it necessary to thread my way through a wealth of sources, both philosophical and mathematical; and it is inevitable that a number of topics have not received the attention they deserve. Still, the thread itself, if tangled in places, has been luminous. "Only connect... Live in fragments no longer," says E. M. Forster, and that is what I have striven for here. (John L. Bell)