Catastrophe theory is an attempt to establish mathematical models for a variety of ""tense"" situations, whether they occur in physics, chemistry, biology, psychology, sociology, or economics. It is based on analyzing variables which have a potential for undergoing a smooth or continuous change but which, under certain conditions, may undergo a drastic discontinuity, a ""singularity"" in the mathematical sense. Or, as the inventors choose to call it, a ""catastrophe."" Thus, a child's metal ""cricket"" snapper may be pressed smoothly but at a certain point the metal pops from convexity to concavity emitting the click sound. The mathematics governing such events derives from topology, which deals with the qualities of curves or geometric shapes which are invariant under a variety of deformations (such as pinching, stretching, etc.). The theory is the brainchild of a French mathematician, Rent Thom, and, in slightly altered form, of an English mathematician, E. Christopher Zeeman. This little book is a lively introduction to the basic ideas and the personalities who developed them. It also provides examples of applications that have been made so far. Though enthusiastic about the ingenuity and potential of the theory, it is fair in describing current criticism of the theory's relevance to real-life situations. One slim volume won't settle the issues, but will serve to explain the theory (whose name itself is controversial) to a larger audience and stimulate further discussion.