The body of mathematics developed in the last forty years or so which
can be put under the heading Singularity Theory is quite large. And the
excellent introductions to this vast sub- ject which are already
available (for instance [AGVJ, [BGJ, [GiJ, [GGJ, [LmJ, [Mr],
[WsJ or the more advanced [Ln]) cover necessarily only apart of even
the most basic topics. The aim of the present book is to introduce the
reader to a few important topics from ZoaaZ Singularity Theory. Some of
these topics have already been treated in other introductory books (e.g.
right and contact finite determinacy of function germs) while others
have been considered only in papers (e.g. Mather's Lemma, classification
of simple O-dimensional complete intersection singularities,
singularities of hyperplane sections and of dual mappings of projective
hypersurfaces). Even in the first case, we feel that our treatment is
different from the introductions mentioned above - the general reason
being that we give special attention to the aompZex anaZytia situation
and to the connections with AZgebraia Geometry. We offer now a detailed
description of the contents, pOint- ing out special aspects and new
material (i.e. previously un- published, though for the most part surely
known to the ts!). Chapter 1 is a short introduction for the beginner.
We recall here two basic results (the Submersion Theorem and Morse
Lemma) and make a few comments on what is meant by the local behaviour
of a function or of a plane algebraic curve.
