"The understanding of quantum matter in and out of equilibrium is among the biggest challenges of modern physics. Despite decades of research fundamental questions, such as the preciseworkings behind rather ubiquitous materials such as high temperature superconductors are still unresolved. At the same time there is a new generation of experiments approaching which realises and probes quantum matter with novel and exotic interactions at an unprecedented level of precision. This has already highlighted new avenues of research but also demands for radically new theoretical approaches which lie outside the scope of just a single traditional physical discipline. Novel and in particular multidisciplinary lines of thinking are required to tackle this immense challenge. Such new research will not solely be delivering invaluable insights into currently unresolved problems but rather form a new basis for the understanding of quantum matter from a multidisciplinary perspective. This will open up new horizons for fundamental research and at the same time will pave the way for future technologies and materials which rely on non-equilibrium phenomena or quantum matter. This research proposal takes on this challenge by setting up a broad theoretical research programme which is multipronged and multidisciplinary and which directly connects to the most recent research efforts in ultra cold atomic physics. Here currently a step change is taking place where new experiments explore strongly correlated quantum physics within gases of excited atoms – so-called Rydberg atoms. Exploiting this unique moment we will develop a framework for the description of the equilibrium and non-equilibrium properties of these complex and very versatile quantum systems. This system-specific research approach has the advantage that theoretical predictions can be verified experimentally and applied in practice almost immediately, leading to research attacking the frontiers of current knowledge."