Combinatorics on words is a field that has grown separately within several branches of mathematics, such as number theory, group theory or probability theory, and appears frequently in problems of theoretical computer science, as dealing with automata and formal languages.

A unified treatment of the theory appeared in Lothaire's Combinatorics on Words. Since then, the field has grown rapidly. This book presents new topics of combinatorics on words.

Several of them were not yet ripe for exposition, or even not yet explored, twenty years ago. The spirit of the book is the same, namely an introductory exposition of a field, with full proofs and numerous examples, and further developments deferred to problems, or mentioned in the Notes.

This book is independent of Lothaire's first book, in the sense that no knowledge of the first volume is assumed. In order to avoid repetitions, some results of the first book, when needed here, are explicitly quoted, and are only referred for the proof to the first volume.

This volume presents, compared with the previous one, two important new features. It is first of all a complement in the sense that it goes deeper in the same direction. For example, the theory of unavoidable patterns (Chapter 3) is a generalization of the theory of square-free words and morphisms. In the same way, the chapters on statistics on words and permutations (Chapters 10 and 11) are a continuation of the chapter on transformations on words of the previous volume.