### Abstract

Random objects such as clusters in the plane can often be described in terms of the conformal mappings which take their boundaries into some standard shape. As the clusters grow, the mapping function changes in a well-defined manner, which is often easier to understand than the original problem. One of the simplest examples is Stochastic Loewner Evolution (SLE), which turns out to describe random curves in equilibrium statistical mechanics models. These lectures will give an introduction to the use of such conformal mappings, and to SLE in particular, from the physicist's point of view.