This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems.All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin.The themes of the book cover important recent developments on- Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology- Geometric Modelling- Image Based Visualization- Software Environments and Applications- Education and CommunicationThe variety of topics makes the book a suitable resource for researchers, lecturers, and practitioners; http://www-sfb288.math.tu-berlin.de/vismath/