The papers in this volume are based on lectures given at the IMA Workshop on Grid Generation and Adaptive Algorithms held during April 28 May 2, 1997. Grid generation is a common feature of many computational tasks which require the discretization and representation of space and surfaces. The papers in this volume discuss how the geometric complexity of the physical object or the non uniform nature of the solution variable make it impossible to use a uniform grid. Since an efficient grid requires knowledge of the computed solution, many of the papers in this volume treat how to construct grids that are adaptively computed with the solution.