This book is a collection of more than 500 attractive open problems in the field and is more up-to-date than any of the competitive books. It is the result of a 25-year-old project initiated by the late Leo Moser. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research. The book's authors are leaders in the field of discrete geometry.