The theory of algebraic semigroups began formally in the 1920s in the work of Suschkewitsch (see, e.g., [S]), although it traces it roots to even earlier work. In the 1960s, Alfred H. Clifford and Gordon B. Preston wrote a two-volume work on the algebraic theory of semigroups [CP] which played a fundamental role in laying out the basics of the theory. That treatise remains the most authoritative work in the area to this day, and its authors, particularly Professor Clifford, are viewed as the founding fathers of the area. Due to recent advances in theoretical computer science as well as other areas of application, algebraic semigroup theory has assumed a role of increasing importance in recent years. Because of his long association with Tulane University, whose mathematics department emerged as a center for research largely during Professor Clifford's most active years, and because Tulane long has been viewed as a national and international center for research in the algebraic and topological theory of semigroups, the Mathematics Department decided to host a conference commemorating Professor Clifford's contributions to the area.

The Conference on the Theory of Semigroups and Its Applications took place in March, 1994, but rather than seeking to reminisce over Professor Clifford's long and distinguished career, the object of the Conference was to identify the state of the theory at that time, and to look forward by identifying those areas of research where semigroup theory can play an important rôle.