Paul Erdös believed that a book of his open problems was perhaps his most important project. He worked on it for years together with his friend and coauthor, whose famously busy travel schedule, countless talks and papers affected the completion date of the book. It will now be finished based exclusively on the selection of problems, their motivations and historical sketches that Paul shared with Alexander during the years of this work. The book will also be a tribute to Paul Erdös, who passed on like a mathematical soldier on duty during a September 1996 mathematical conference in Warsaw.