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By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents:PrefaceMathematical symbolsNumber-theoretical dynamical systemsBasic ergodic theoryRenewal theory and -sum-level setsInfinite ergodic theoryApplications of infinite ergodic theoryBibliographyIndex