The course is an introductory course to ergodic theory with an emphasis on entropy theory. In ergodic theory, the relevant structure is that of a measure space, and we will mostly focus on the case of probability measure spaces. These have a very rich theory on their own and have had some remarkable applications that seem to have nothing to do with ergodic theory: for instance Margulis Normal Subgroup Theorem, Furstenberg's proof of Szemeredi's Theorem, etc.