This course is intended to explain the main concepts in ergodic theory to a non-specialised, yet mathematically erudite, audience. With this in mind, I will begin by explaining the background in measure theory required.
Then, I will explain some of the main results in classical ergodic theory (on measure spaces). Subsequently, I will discuss some of the developments in the past 40 years in Smooth Ergodic Theory (on manifolds) and, finally, try to give a flavour of some recent work.