ABSTRACT
Abstract This chapter aims at being a crash course on max-stable processes with an emphasis on their use for modeling spatial extremes. We will see how max-stable processes are defined through a simple spectral representation and how it is possible to derive the finite dimensional distributions from it. Because the goal of this crash course is also to be of practical interest, existing parametric max-stable models will be introduced and discussed. A useful measure of spatial dependence, the extremal coefficient function, will be introduced as well as several approaches to fit max-stable processes to spatial data. Finally we open the discussion with other alternatives to max-stable processes to model spatial extremes.
