This volume collects the papers accepted for presentation at the 10th IMA C- ference on the Mathematics of Surfaces, held at the University of Leeds, UK, September 15¿17, 2003. As with all earlier conferences in the series, contributors to this volume come from a wide variety of countries in Asia, Europe and North America. The papers presented here re?ect the continued relevance of the s- ject, and, by comparison with the contents of earlier volumes in the series, the changing nature of application areas and mathematical techniques. To give the casual browser of these proceedings an idea of the diversity of the subject area, the papers in the present volume cover such topics and techniques as digital geometry processing, computer graphics, surface topology, medical applications, subdivision surfaces, surface reconstruction, surface triangulation, waterma- ing, data compression, data smoothing, human-computer interaction, extracting shapeformshading,surfaceheightrecovery,reverseengineering,box-splines,the Plateau Problem, splines (a variety of papers), trans?nite blending, and a?ne arithmetic. There is also a paper in memory of the late Prof. Josef Hoschek of theTechnischeUniversit¿ atDarmstadt,co-authoredbyaformerresearchstudent, Prof. Bert Juttler, ¿ on the subject of using line congruences for parameterizing special algebraic surfaces. We would like to thank all those who attended the conference and helped to makeitasuccess. Inparticularwethankthosewhocontributedtotheseproce- ings.