This volume presents the core of invited expository lectures given at the 1993 NATO ASI held at the University of York. The subject matter of the ASI was the interplay between automata, semigroups, formal languages and groups. The invited talks were of an introductory nature but at a high level and many reached the cutting edge of research in the area. The lectures were given to a mixed group of students and specialists and were designed to be accessible to a broad audience. The papers were written in a similar spirit in the hope that their readership will be as wide as possible. With one exception they are all based on the talks which the lecturers gave at the meeting. The exception is caused by the fact that due to unanticipated progress the topic of John Rhodes' talk is now in such a state of flux that it has not been possible to produce a paper giving a clear picture of the situation. However, we do include an article by a member of the "Rhodes school" , namely Christopher Nehaniv, expanding on a contributed talk he gave. It generalizes the celebrated Krohn-Rhodes theorem for finite semigroups to all semigroups. For many years there has been a strong link between formal language theory and the theory of semigroups. Each subject continues to influence the other.