Almost every scientist has heard of catastrophe theory and knows that there has been a considerable amount of controversy surrounding it. Yet comparatively few know anything more about it than they may have read in some article written for the general public. The aim of this book is to make it possible for anyone with only a modest background in mathematics – no more than is usually included in a first year university course for students not specializing in the subject – to understand the theory well enough to follow the arguments in papers in which it is used and, if the occasion arises, to use it himself.

Most readers will find a number of concepts which are new to them; it would have been impossible to avoid this altogether and still give an adequate account of the theory. But wherever possible I have tried to keep to familiar ground. My object is to explain the theory, rather than to provide formal proofs, and it is almost always harder to understand anything if it is explained in terms of ideas which have themselves only just been introduced. For the same reason, I have sometimes carried out calculations by brute strength and awkwardness when a more elegant derivation was available. I have, however, tried to keep to the spirit, if not always the letter, of the mathematics, and the reader who uses this book as an introduction and then goes on to study the theorems in their full rigour should find that there is nothing he has to unlearn.