Combinatorics on words is a field that has grown separately within several branches of mathematics, such as group theory or probabilities, and appears frequently in problems of computer science dealing with automata and formal languages. It may now be considered as an independent theory because of both the number of results that it contains and the variety of possible applications.

This book is the first attempt to present a unified treatment of the theory of combinatorics on words. It covers the main results and methods in an elementary presentation and can be used as a textbook in mathematics or computer science at undergraduate or graduate level. It will also help researchers in these fields by putting together a lot of results scattered in the literature.

The idea of writing this book arose a few years ago among the group of people who have collectively realized it. The starting point was a mimeo-graphed text of lectures given by M. P. Schützenberger at the University of Paris in 1966 and written down by J. F. Perrot. The title of this text was “Quelques Problèmes combinatoires de la théorie des automates.” It was widely circulated and served many people (including most of the authors of this book) as an introduction to this field.