This book, "Ergodic Theory on Compact Spaces," is a collection of lecture notes edited by A. Dold and B. Eckmann, published as volume 527 in the Lecture Notes in Mathematics series. The authors are Manfred Denker, Christian Grillenberger, and Karl Sigmund, all experts in the field of ergodic theory. The book provides a comprehensive overview of ergodic theory on compact spaces, covering various aspects of topological dynamics, invariant measures, time averages, ergodicity, mixing, shifts, entropy, and more. The content is structured into 31 chapters, starting with an introduction to measure-theoretic dynamical systems and measures on compact metric spaces. It then delves into invariant measures, time averages, ergodicity, mixing, and transitivity. The latter part of the book discusses shifts and subshifts, partitions and generators, information and entropy, and the computation of entropy. It also covers entropy for Bernoulli and Markov shifts, ergodic decompositions, topological entropy, and expansive homeomorphisms. The book includes detailed discussions on subshifts of finite type, the variational principle for topological entropy, measures with maximal entropy, and the specification property. It also addresses basic sets for axiom A, automorphisms of the torus, and various embedding theorems for aperiodic transformations. The book concludes with a bibliography and an index, along with a list of symbols. The book is a valuable resource for researchers and students in the field of ergodic theory and topological dynamics, offering a thorough treatment of the subject with a focus on compact spaces. It is published by Springer-Verlag and is available in both German and English.This book, "Ergodic Theory on Compact Spaces," is a collection of lecture notes edited by A. Dold and B. Eckmann, published as volume 527 in the Lecture Notes in Mathematics series. The authors are Manfred Denker, Christian Grillenberger, and Karl Sigmund, all experts in the field of ergodic theory. The book provides a comprehensive overview of ergodic theory on compact spaces, covering various aspects of topological dynamics, invariant measures, time averages, ergodicity, mixing, shifts, entropy, and more. The content is structured into 31 chapters, starting with an introduction to measure-theoretic dynamical systems and measures on compact metric spaces. It then delves into invariant measures, time averages, ergodicity, mixing, and transitivity. The latter part of the book discusses shifts and subshifts, partitions and generators, information and entropy, and the computation of entropy. It also covers entropy for Bernoulli and Markov shifts, ergodic decompositions, topological entropy, and expansive homeomorphisms. The book includes detailed discussions on subshifts of finite type, the variational principle for topological entropy, measures with maximal entropy, and the specification property. It also addresses basic sets for axiom A, automorphisms of the torus, and various embedding theorems for aperiodic transformations. The book concludes with a bibliography and an index, along with a list of symbols. The book is a valuable resource for researchers and students in the field of ergodic theory and topological dynamics, offering a thorough treatment of the subject with a focus on compact spaces. It is published by Springer-Verlag and is available in both German and English.