**Preface**
A NATO Advanced Research Workshop "Computational Commutative and
Non-Commutative Algebraic Geometry" was held in Chishinau, Moldova from 6 to 11
June, 2004. The financial support was offered by the NATO grant PST.ARW.980392.
The workshop was organized by Gerhard Pfister and Svetlana Cojocaru with
assistance of members of the Organizing Committee: Jürgen Herzog, Lorenzo
Robbiano, Victor Ufnarovski. There were 25 lectures given by the participants
and open discussions on the subjects presented. The central theme of this
workshop was the interplay between commutative and noncommutative algebraic
geometry, with its theoretical and computational aspects. The Scientific
Program emphasizes current trends in Commutative and Non-Commutative Algebraic
Geometry and Algebra. The contributors to this volume review the state of the
art and present new evolution and progress reflecting the topics discussed in
the lectures. The volume addresses in the first place researchers and graduate
students. The editors would like to thank the contributors to this volume.
Thanks are due to the NATO Public Diplomacy Division for their generous
financial support. Special thanks to Tatiana Verlan, who had the task to
correct and prepare the manuscript.

December 2004, Svetlana Cojocaru, Gerhard Pfister, Victor
Ufnarovski