The first one will be devoted to the complex analytic background needed. In particular Koebe theorem will be revisited as well as capacity theory. The classical Loewner theory will be presented in detail as well as the application to the third coefficient in the Bieberbach conjecture.

The second part will start with a crash course in stochastic processes. Stochastic Loewner evolution SLE(k) will then be defined and the different phases according to the value of k will be discussed.

The third part is devoted to the application of the theory to percolation, the harmonic explorer, Laplacian random walk, etc. A particular stress will be given on the conformally invariant features of these processes.