Translated from the popular French edition the goal of the book is to provide a self-contained
introduction to mean topological dimension an invariant of dynamical systems introduced in
1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon
Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of
minimal dynamical systems into shifts. A large number of revisions and additions have been made
to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey
line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean
topological dimension for continuous actions of countable amenable groups. These new chapters
contain material that have never before appeared in textbook form. The chapter on amenable
groups is based on Følner's characterization of amenability and may be read independently from
the rest of the book. Although the contents of this book lead directly to several active areas
of current research in mathematics and mathematical physics the prerequisites needed for
reading it remain modest essentially some familiarities with undergraduate point-set topology
and in order to access the final two chapters some acquaintance with basic notions in group
theory. Topological Dimension and Dynamical Systems is intended for graduate students as well
as researchers interested in topology and dynamical systems. Some of the topics treated in the
book directly lead to research areas that remain to be explored.
