From the Preface by D. Ruelle: "...Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems.'' For this printing of R. Bowen's book, J.-R. Chazottes has rekeyed it in TeX for easier reading, thereby correcting typos and bibliographic details.