This classic survey paper is an introduction to some difficult contemporary fields of study in mathematics known under the rubric of Catastrophe Theory, which encompasses the theory of "typical" singularities of functions and mappings. The authors discuss the basic ideas, concepts and methods of the theory of singularities and the survey is presented in three sections:
Section 1: Singularities of Functions, Caustics and Wave Fronts
Section 2: Integrals of the Stationary Phase Method
Section 3: The Geometry of Formulas
The survey provides a useful source of reference for students, postgraduates and researchers in these areas of mathematics.