In this volume the authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. The editors include papers that survey Clifford's work on Clifford semigroups and trace the influence of Clifford's work on current semigroup theory. Also notable is a paper on applications from other areas of mathematics to semigroup theory, and a paper on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable.