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This IMA Volume in Mathematics and its Applications GRID GENERATION AND ADAPTIVE ALGORITHMS is based on the proceedings of a workshop with the same title. The work- shop was an integral part of the 1996-97 IMA program on "MATHEMAT- ICS IN HIGH-PERFORMANCE COMPUTING. " I would like to thank Marshall Bern (Xerox, Palo Alto Research Cen- ter), Joseph E. Flaherty (Department of Computer Science, Rensselaer Polytechnic Institute), and Mitchell Luskin (School of Mathematics, Uni- versity of Minnesota), for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda- tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr. , Professor and Director v PREFACE Scientific and engineering computation has become so complex that traditional numerical computation on uniform meshes is generally not pos- sible or too expensive. Mesh generation must reflect both the domain geometry and the expected solution characteristics. Meshes should, fur- thermore, be related to the solution through computable estimates of dis- cretization errors. This, suggests an automatic and adaptive process where an initial mesh is enriched with the goal of computing a solution with prescribed accuracy specifications in an optimal manner. While automatic mesh generation procedures and adaptive strategies are becoming available, major computational challenges remain. Three-dimensional mesh genera- tion is still far from automatic.