The thematic term on Semigroups, Algorithms, Automata and Languages organized at the International Centre of Mathematics (Coimbra, Portugal) in May-July 2001 was the gathering point for researchers working in the field of semigroups, algorithms, automata and languages. These areas were selected considering their huge recent developments, their potential applications, and the motivation from other fields of mathematics and computer science. This proceedings volume is a collection of advanced courses and original contributions on semigroups and their connections with logic, automata, languages, group theory, discrete dynamics, topology and complexity. A selection of open problems discussed during the thematic term is also included.