Measure preserving systems: ergodicity, recurrence, ergodic theorems, mixing.
Invariant measures for continuous maps. Ergodic decomposition, unique ergodicity.
Conditional measures, general ergodic decomposition. Factors and joinings. The Kronecker factor. Construction of joinings.
Actions of locally compact groups: ergodicty and mixing, Haar measure, Amenable groups, more topics as time allows.
The course will follow the book [Einsiedler, Manfred; Ward, Thomas. Ergodic theory with a view towards number theory], focusing on chapters 2, 4, 5, 6 and 8.