A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.

Preface; Part I. Rational Series: 1. Rational series; 2. Minimization; 3. Series and languages; 4. Rational expressions; Part II. Arithmetic: 5. Automatic sequences and algebraic series; 6. Rational series in one variable; 7. Changing the semiring; 8. Positive series in one variable; Part III. Applications: 9. Matrix semigroups and applications; 10. Noncommutative polynomials; 11. Codes and formal series; 12. Semisimple syntactic algebras; Open problems and conjectures; References; Index of notation; Index.

Jean Berstel is Emeritus Professor of Computer Science in the Gaspard-Monge Institute at Université Paris-Est, France.