This book is a tribute to Paul ErdHs, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines -- within the context of his unique personality and lifestyle -- the legacy of open problems he left to the world after his death in 1996. Unwilling to succumb to the temptations of money and position, ErdHs never had a home and never held a job. His "home" was a bag or two containing all his belongings and a record of the collective activities of the mathematical community. His "job" was one at which he excelled:...