Understanding the many-body physics of strongly correlated systems has always been a major challenge for theoretical and experimental physics. The recent advances in the field of ultracold quantum gases have opened a completely new way to study such strongly correlated systems. It is now feasible to use ultracold gases as quantum simulators for such diverse systems such as the Hubbard model or the BCS-BEC crossover. The objective of this project is to study a three-component Fermi gas in an optical lattice, a system with rich many-body physics. With our experiments we aim to contribute to the understanding of exotic phases which are discussed in the context of QCD and condensed matter physics.