Statistical Physics, together with Quantum Mechanics, is the pillar of our understanding of many physical phenomena, from the simplest to the more sophisticated ones. It addresses, for instance, crucial questions about the nature of the phase transitions and foresees the possibility to forge new states of matter, as Bose-Einstein condensation in ultra-cold gases. At the same time, Statistical Physics provides a vital source of fresh ideas and inspirations for those working in more theoretical directions, e.g. quantum field theory, exactly solved models, random matrices, complex systems, probability, topological quantum computation. Its attraction lies in its ability to produce an array of sophisticated analytical and conceptual tools with far reaching applications. This remarkable blend of mathematical and physical ideas is at the root of the outstanding scientific elegance and extraordinary efficiency that characterize this scientific area. The main purpose of this PhD is to lead an intense training and research program on the fundamental questions posed by this rapidly evolving research area. Their answer will result in a more profound comprehension of the novel aspects of matter and, simultaneously, in a promotion of a new generation of researchers open to the deep interdisciplinary aspects of science.