From 18 to 20 October 2004, a conference “Singularities and Computer Algebra” was held at the University of Kaiserslautern on the occasion of Gert-Martin Greuel's 60th birthday. It was attended by 70 participants from Europe, Israel, Japan, Canada and the U.S.A. We were particularly happy that Greuel's teacher, Egbert Brieskorn, was among them.

Most of the participants have been inuenced by Greuel's work on singularities and their computational aspects over the last 30 years. Among them, one could find colleagues and friends from the early years in Göttingen and Bonn, but also former and present diploma and Ph.D. students of Gert-Martin Greuel at Kaiserslautern. In particular, each of the invited speakers could look retrospectively at cooperating in one way or another with Greuel.

The papers of this volume concern ten of the invited lectures, supplemented by four articles which are written by participants of the conference and focus on computational aspects. Most of the contributions are intended to give an overview on a particular aspect of singularities. They describe the development of important areas of singularity theory over the past years and they discuss open questions.

In the lead text, we include a list of the invited lectures and a list of the participants as well as a picture of the septic with 99 nodes found by Oliver Labs and Duco van Straten, which has acted as a logo for the conference. Further, we include an article focussing on Aspects of Gert-Martin Greuel's Mathematical Work.