This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition – with full proofs – of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.

‘This substantial monograph comprises the first thorough and self-contained exposition of the theory of dimension groups in topological dynamics … It is a welcome addition to the dynamics literature in an area of much activity with links to several other disciplines, including operator algebras and computer science.’

Thomas B. Ward Source: zbMATH

‘… an impressive self-contained expository presentation that explores the connections between properties of topological dynamical systems and their dimension groups. The book is a rich source of material on topological and symbolic dynamics and will be useful for both graduate students in mathematics or computer science and experienced researchers.’

Olena Karpel Source: MathSciNet