Statistical mechanics is the branch of physics that attempts to understand the laws of the behaviour of systems that are composed of very many individual components, such as gases, liquids, or crystalline solids. The statistical mechanics of disordered systems is a particularly difficult, but also particularly exciting, branch of the general subject, that is devoted to the same problem in situations when the interactions between these components are very irregular and inhomogeneous, and can only be described in terms of their statistical properties. From the mathematical point of view, statistical mechanics is, in the spirit of Dobrushin, a ‘branch of probability theory’, and the present book adopts this point of view, while trying not to neglect the fact that it is, after all, also a branch of physics.

This book grew out of lecture notes I compiled in 2001 for a Concentrated Advanced Course at the University of Copenhagen in the the MaPhySto programme and that appeared in the MaPhySto Lecture Notes series in the same year. In 2004 I taughta two-semester course on Statistical Mechanics at the Technical University of Berlin with in the curriculum of mathematical physics for advanced undergraduate students, both from thephysics and the mathematics departments. It occurred to me that the material I was going to cover in this course could indeed provide a suitable scope for a book, in particular as the mathematical understanding of the field was going through a period of stunning progress, and that an introductory textbook, written from a mathematical perspective, was maybe more sought after than ever.