Preface to the Second Edition (2006)

Summary

The First Edition (1981) of “Synthetic Differential Geometry” has been out of print since the early 1990s. I felt that there was still a need for the book, even though other accounts of the subject have in the meantime come into existence.

Therefore I decided to bring out this Second Edition. It is a compromise between a mere photographic reproduction of the First Edition, and a complete rewriting of it. I realized that a rewriting would quickly lead to an almost new book. I do indeed intend to write a new book, but prefer it to be a sequel to the old one, rather than a rewriting of it.

For the same reason, I have refrained from attempting an account of all the developments that have taken place since the First Edition; only very minimal and incomplete pointers to the newer literature (1981– 2006) have been included as “Notes 2006” at the end of each of the Parts of the book.

Most of the basic notions of synthetic differential geometry were already in the 1981 book; the main exception being the general notion of “strong infinitesimal linearity” or “microlinearity”, which came into being just too late to be included. A small Appendix D on this notion is therefore added.