The RSS-programme moves at the interface between probability theory and statistical physics. It focusses on the study of systems consisting of a large number of interacting random components. These components interact with each other and with their environment. Even when the interaction is local and simple, such systems typically exhibit a global and complex behaviour, with a long-range dependence resulting in anomalous fluctuations and phase transitions. The mathematical understanding of systems with interacting random components requires the use of powerful probabilistic ideas and techniques. The challenge is to work with basic models serving as paradigms and to unravel the complex "random spatial structures" arising in these models. Statistical physics provides the conceptual ideas, while probability theory provides the mathematical language and framework. The important challenge is to give a precise mathematical treatment of the rich macroscopic physics that arises from the underlying microscopic dynamics. Key topics researched within the RSS-programme are: phase transitions, critical exponents, mean-field behavior, percolation, polymers, spin glasses, metastability, geometry of random networks, random processes on random networks, multi-type populations, catalytic particle systems. The RSS-programme focusses on four themes: * Critical phenomena * Disordered media * Random networks * Population dynamics Mathematical statistical physics is an interdisciplinary research area that deals with the modelling of complex random processes from a variety of different perspectives.