Since his death in 1996, many scientific meetings have been dedicated to the memory of Paul ErdAs. From July 4 to 11, 1999, the conference "Paul ErdAs and his Mathematics" was held in Budapest, with the ambitious goal of showing the whole range of ErdAs' work - a difficult task in view of ErdAs' versatility and his broad scope of interest in mathematics. According to this goal, the topics of lectures, given by the leading specialists of the subjects, included number theory, combinatorics, analysis, set theory, probability, geometry and areas connecting them, like ergodic theory. The conference has contributed to changing the common view that ErdAs worked only in combinatorics and combinatorial number theory. In the present two volumes, the editors have collected, besides some personal reminiscences by Paul's old friends, mainly survey articles on his work, and on areas he initiated or worked in.