These lecture notes, titled "Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms," were prepared from a course given at the University of Minnesota and revised during the author's Sloan Fellowship. The book is edited by A. Dold and B. Eckmann and published as part of the Lecture Notes in Mathematics series, volume 470. The author is Prof. Rufus Bowen of the University of California, Berkeley. The book explores equilibrium states and the ergodic theory of Anosov diffeomorphisms. It covers topics such as Gibbs measures, Ruelle's Perron-Frobenius theorem, the variational principle, and thermodynamic formalism. It also discusses axiom A diffeomorphisms, including their definitions, spectral decomposition, Markov partitions, and symbolic dynamics. The text further examines the ergodic theory of axiom A diffeomorphisms, focusing on equilibrium states for basic sets, the case where the potential function is a function of the position, and the relationship between attractors and Anosov diffeomorphisms. The book is structured with an introduction, followed by chapters on Gibbs measures, general thermodynamic formalism, axiom A diffeomorphisms, and the ergodic theory of axiom A diffeomorphisms. Each chapter includes subsections that delve into specific aspects of the subject. The work is supported by a bibliography and an index. It is published by Springer-Verlag and is available in both German and English. The book is dedicated to the study of dynamical systems, particularly focusing on the properties of Anosov diffeomorphisms and their equilibrium states. The content is intended for advanced students and researchers in mathematics, particularly those interested in ergodic theory and dynamical systems.These lecture notes, titled "Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms," were prepared from a course given at the University of Minnesota and revised during the author's Sloan Fellowship. The book is edited by A. Dold and B. Eckmann and published as part of the Lecture Notes in Mathematics series, volume 470. The author is Prof. Rufus Bowen of the University of California, Berkeley. The book explores equilibrium states and the ergodic theory of Anosov diffeomorphisms. It covers topics such as Gibbs measures, Ruelle's Perron-Frobenius theorem, the variational principle, and thermodynamic formalism. It also discusses axiom A diffeomorphisms, including their definitions, spectral decomposition, Markov partitions, and symbolic dynamics. The text further examines the ergodic theory of axiom A diffeomorphisms, focusing on equilibrium states for basic sets, the case where the potential function is a function of the position, and the relationship between attractors and Anosov diffeomorphisms. The book is structured with an introduction, followed by chapters on Gibbs measures, general thermodynamic formalism, axiom A diffeomorphisms, and the ergodic theory of axiom A diffeomorphisms. Each chapter includes subsections that delve into specific aspects of the subject. The work is supported by a bibliography and an index. It is published by Springer-Verlag and is available in both German and English. The book is dedicated to the study of dynamical systems, particularly focusing on the properties of Anosov diffeomorphisms and their equilibrium states. The content is intended for advanced students and researchers in mathematics, particularly those interested in ergodic theory and dynamical systems.