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. PrefaceMathematical symbolsNumber-theoretical dynamical systemsBasic ergodic theoryRenewal theory and a -sum-level setsInfinite ergodic theoryApplications of infinite ergodic theoryBibliographyIndex