The emergence of singularity theory marks the return of mathematics to the study of the simplest analytical objects: functions, graphs, curves and surfaces. The modern singularity theory for smooth mappings, which is undergoing intensive developments, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry and topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). The papers in this volume include reviews of established areas as well as presentations of results in singularity theory. The contributors have emphasized examples and discussion of results, rather than burying the ideas in formalism, notation and technical details. The aim is to introduce all mathematicians - as well as physicists, engineers and other consumers of singularity theory - to the world of ideas and methods in this burgeoning area.
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