From the very beginning, algebraic topology has developed under the influ ence of the problems posed by trying to understand the topological properties of complex algebraic varieties (e.g., the pioneering work by Poincare and Lefschetz). Especially in the work of Lefschetz Lf2], the idea is made explicit that singularities are important in the study of the topology even in the case of smooth varieties. What is known nowadays about the topology of smooth and singular vari eties is quite impressive. The many existing results may be roughly divided into two classes as follows: (i) very general...

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).

This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf (as opposed to constant)coefficients.

The first 5...

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...