A microscopic view on synthetic quantum matter Markus Greiner Department of Physics, Harvard University With quantum gas microscopy we are now able to take the control of ultracold quantum gases in an optical lattice to the next and ultimate level of high fidelity addressing, manipulation and readout of single particles. In my talk I will first give an introduction to this field of research and present an overview of recent experiments, including the first observation of an anti-ferromagnetic phase of Fermions in an optical lattice.