  These are notes for a mini-course on the extremes of correlated random fields
which I gave in the spring 2013 in Marseille. The first chapter recalls the
paradigmatic random energy models with finitely many scales introduced by B.
Derrida in the context of mean field spin glasses. The second chapter presents
a multi-scale refinement of the second moment method which is particularly
efficient to analyze models with a growing number of scales, such as the
Gaussian hierarchical field (the directed polymer on Cayley trees). In the
third chapter, applications of the method to e.g. Gaussian free fields and
issues of percolation in high dimensions are briefly touched upon. The last
chapter deals with a procedure of "local projections" which allows, in a number
of cases, to construct scales from first principles.
