In the spring term of 1980 I gave a course on singularities at Yale University (while supported by NSF grant MCS 7905018), which provided the basis of a set of notes prepared for the first two years of the Singularity Intercity Seminar (1980 – 1982, at Leiden, Nijmegen and Utrecht, jointly run with Dirk Siersma and Joseph Steenbrink). These notes developed into the present book. As a consequence, aim and prerequisites of the seminar and this book are almost identical.

The purpose of the seminar was to introduce its participants to isolated singularities of complex spaces with particular emphas is on complete intersection singularities. When we started we felt that no suitable account was available on which our seminar could be based, so it was decided that I should supply notes, to be used by both the lecturers (in preparing their talks) and the audience. This was quite a purifying process: many errors and inaccuracies of the first draft were thus detected (and often corrected).

The prerequisites consisted of some algebraic and analytic geometry (roughly covering the contents of the books of Mumford (1976) and Narasimhan (1966)), some algebraic topology (as in Spanier (1966) and Godement (1958)) and some facts concerning Stein spaces. Given this background, my goal was to prove every assertion in the text. This has been achieved except for the coherence theorem (8.7) and some assertions in the descriptive chapter 1.