This book is an outgrowth of a book on quantum gravity that the author started to write nine years ago in collaboration with Christopher Isham. It began as an Appendix to the quantum gravity book, but subsequent developments modified the original plan. Firstly, new results in quantum gravity, particularly in supergravity and in the applications of topology to quantum field theory, appeared so rapidly that the timing of the collaborative volume became inopportune. Secondly, the theory of supermanifolds had so many loose ends which needed to be dealt with that the original Appendix grew beyond reasonable size limits and turned into a book in its own right.

A previous generation of theoretical physicists could function adequately with a knowledge of the theory of ordinary manifolds and ordinary Lie groups. With the discovery of Bose–Fermi supersymmetry all this changed. Nowadays the theorist must know about supermanifolds and super Lie groups. The purpose of the present volume is to provide him with an easily accessible account of these mathematical structures. Mathematicians will find much of this book incomplete and expressed in language that they have nowadays passed beyond, but it is probably pitched about right for the average physicist. It still has something of the character of an Appendix in its lack of any account of how it relates to supergravity and other locally supersymmetric theories.