This project addresses fundamental issues in the study of nucleus-nucleus collisions at high energy, such as the thermodynamics of matter at extremely high temperature, or the dynamics of the dense system of gluons that constitute most of the wave-function of a nucleus at asymptotically high energy. In either case, one is dealing with strongly interacting systems whose description requires the development of new theoretical tools.The Relativistic Heavy Ion Collider (RHIC) in the USA has deeply changed our vision of hot and dense matter, revealing for instance that the quark-gluon plasma produced in heavy ion collisions behaves as a strongly coupled liquid with a relatively small viscosity. Soon, beams of lead nuclei will be accelerated at the Large Hadron Collider (LHC) at CERN, with energies exceeding by more than one order of magnitude those of RHIC. New phenomena are likely to be observed, and one of the goals of the project is to develop the theoretical tools that will be needed to understand these phenomena: by developing new, non perturbative methods of quantum field theory in order to calculate the properties of the quark-gluon plasma and the initial nuclear wavefunctions; by providing the appropriate theoretical frameworks to interpret the data and possibly suggest new measurements.All members of the proposed research team have made breakthrough contributions to the field. They bring a unique expertise on the various aspects of the project, putting the team in a position to make a groundbreaking contribution. The project has also cross-disciplinary aspects that will be exploited whenever deemed appropriate. This will contribute to broaden the training of the young researchers hired within the project.