Topics include the following:

1. Review of basic measure theory (if necessary)
2. Ergodic theorems. They form the basis of ergodic theory and use the first dynamical idea: taking averages over time and comparing them to space averages.
3. Mixing properties: weak mixing and mixing are stronger then ergodicity.
4. Unique ergodicity: The equivalent conditions to having only one invariant measure are discussed and, in the case of a translation on a torus, applied.
5. Entropy theory: After the basic definitions, entropy is discussed as an isomorphism invariant. The notion of completely positive entropy is studied and compared to other notions. Topological entropy and the variation principle are introduced.
6. Isomorphism theory: Time permitting, the theory of Bernoulli maps and their isomorphism will be discussed.
7. Along the way, many examples of different behavior are studied: mixing--ergodic--nonergodic, symbolic--algebraic--applied, zero entropy--positive entropy, isomorphic systems--nonisomorphic systems.