The document summarizes research on mesh representations in computer graphics. It discusses Greg Turk's introduction of "mutual tessellation" to represent objects at different levels of detail. It also covers Hugues Hoppe's work on "mesh optimization" to minimize triangles in dense meshes and "progressive meshes" to preserve overall appearance while simplifying. The document outlines challenges of mesh simplification, level-of-detail approximations, and compression. It describes representing meshes as sets of vertices, connectivity, and attributes. An energy function is defined to optimize meshes by minimizing distance and spring energies while preserving scalar attributes. Applications in medical imaging and reduced manual work in graphics are mentioned.