Lecture Course I:
Ergodic theory is a powerful set of mathematical tools and ideas used to study the behaviour of dynamical systems in which the behaviour of individual orbits is very complex, while the behaviour of collections of orbits is sufficiently orderly to allow them to be studied using the language of probability or measure theory. This body of work has found diverse applications in dynamical systems, number theory, geometry and many other parts of mathematics. As a branch of mathematics, it is characterised by the great diversity of techniques employed and by a huge diversity of sources of examples and phenomena. This course is intended to equip the students with the language and background for the other two more specialised courses.