These proceedings collect the papers accepted for presentation at the bien- nial IMA Conference on the Mathematics of Surfaces, held in the University of Cambridge, 4-7 September 2000. While there are many international con- ferences in this fruitful borderland of mathematics, computer graphics and engineering, this is the oldest, the most frequent and the only one to concen- trate on surfaces. Contributors to this volume come from twelve different countries in Eu- rope, North America and Asia. Their contributions reflect the wide diversity of present-day applications which include modelling...