Quantum Chromodynamics (QCD) at finite temperature and non-zero density describes phenomena relevant to the early universe and heavy-ion collisions. The applicability of perturbation theory is limited to large temperatures and densities. We plan to use lattice simulations to study QCD thermodynamics. There are different regularizations of QCD on the lattice. The computationally most effective one is the staggered formulation, while Wilson or chiral fermions are theoretically more established. We have to distinguish studies at vanishing baryon densities from the ones concerning non-zero density. At vanishing densities the order of the QCD transition between the hadronic phase and the quark-gluon plasma was studied using staggered fermions. In the physical, continuum limit the transition was found to be a crossover. The transition temperature has also been determined. These studies should be and will be extended using Wilson and chiral fermions. This way the staggered results can be checked. At non-vanishing densities direct lattice simulations are prohibited by the infamous sign problem. Recently the multi-parameter reweighting method was developed to study moderate densities using simulations at zero baryon density. The phase diagram as well as the critical point of QCD was determined using staggered fermions with a single lattice resolution. We plan to extend these studies in two ways. In the first step finer lattices will be studied with staggered fermions and a continuum extrapolation will be attempted. In the second step Wilson and possibly chiral fermions will be used. At large densities where the sign problem is the most severe the density of states method will be used. Based on our experience with PC clusters we will build a new, high performance cluster to achieve these goals. The establishment of a strong new research group certainly will improve the competitivity of the European lattice community.