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Synopsis This is an introductory book on Ergodic theory. The presentation has a slow pace and the book can be read by any person with a background in basic measure theory and metric topology. A new feature of the book is that basic topics of Ergodic theory such as the Poincare recurrence lemma, induced automorphisms and Kakutani towers, compressibility and E. Hopf’s theorem, the theorem of Ambrose on representation of flows are treated at the descriptive set-theoretic level before their measure-theoretic or topological versions are presented. In addition, topics around the Glimm-Effros theorem are discussed. These topics have so far not found a place in texts on Ergodic theory. In the second edition, a section on rank automorphisms and a brief discussion of the Ergodic theorem due to Wiener and Wintner have been added.