An introduction to ergodic theory with an emphasis on entropy theory. Ergodic theory is one branch in mathematical dynamics: the study of group actions on spaces preserving the structure on the space. A key feature is having complicated orbits so that one cannot simply quotient the space by the action. The relevant structure is that of a measure space; we mostly focus on the case of probability measure spaces. These have a 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.