Discrete Geometry is the kind of area in which problems can be quickly expressed and understood by a wide audience, as usually only elementary geometry is involved. This long-awaited book is based on William O.J. Moser's problem collection that has been circulating in the community for many years. The authors state a much extended variety of problems. For each problem they provide the historical background and give comprehensive references. The book will be of great value to any graduate student and researcher in discrete geometry.Bernard Chazelle (Princeton University): "This will be a terrific book. I've had drafts of it over the years, and I can't wait to have the final version. It will be extremely popular in the discrete geometry community (where the authors are undisputed leaders). This project has my highest recommendation." Joel Spencer (NYU): "- Pach has that wonderful "Hungarian" sense of problem posing and solving. ' This is a very exciting project'"