"Among the most defining events in physics during the last decade were the spectacular advances in the field of strongly correlated quantum many body systems: the observation of quantum phase transitions in optical lattices and the realization that many body entanglement can be exploited to build quantum computers are only two of the notable breakthroughs. The description of strongly correlated quantum systems and the associated entanglement structure is still largely unexplored territory. This field represents one of the big challenges and opportunities in theoretical physics. In a recent evolution, we showed that the tools developed in the context of quantum computing and entanglement theory lead to a novel understanding of the structure of the wavefunctions that arise as ground states of strongly correlated quantum Hamiltonians. This approach opens up a wealth of new research opportunities that will be investigated, such as a description of quantum phases of matter with nonlocal order parameters and an explicit characterization of quantum states exhibiting critical behaviour and/or topological quantum order. Such theories cannot be described within the conventional Landau theory of phase transitions. The theory of entanglement also provides a new language in which one can describe real-space renormalization group methods, and this is resulting in a long anticipated extension of their range of applicability. A crucial part of the project will consist of developing stable numerical methods that generalize the very successful DMRG method to two dimensions and to non-equilibrium situations. One of the main objectives is to simulate the phase diagram of the Hubbard model in two dimensions. Preliminary results are promising, and we are confident that this work will impact the way we understand, observe and manipulate the quantum world. This is especially relevant since quantum effects will play an increasingly dominant role in future technologies."