We propose to take the experimental investigation of strongly-correlated quantum matter in the context of ultracold gases to the next scientific level by applying “quantum gas microscopy” to quantum many-body systems with tunable interactions. Tunability, as provided near Feshbach resonances, has recently proven to be a key ingredient for a broad variety of strongly-correlated quantum gas phases with strong repulsive or attractive interactions and for investigating quantum phase transitions beyond the Mott-Hubbard type. Quantum gas microscopy, as recently demonstrated in two pioneering experiments, will be combined with tunability as given by bosonic Cs atoms to give direct access to spatial correlation functions in the strongly interacting regimes of e.g. the Tonks gases, to open up the atom-by-atom investigation of transport properties, and to allow the detection of entanglement. It will provide local control at the quantum level in a many-body system for entropy engineering and defect manipulation. It will allow the generation of random potentials that add to a periodic lattice potential for the study of glass phases and localization phenomena. In a second step, we will add bosonic and fermionic potassium (39-K and 40-K) to the apparatus to greatly enhance the capabilities of the tunable quantum gas microscope, opening up microscopy to fermionic and, in a third step, to fermionic dipolar systems of KCs polar ground-state molecules. In the case of atomic 40-K fermions with tunable contact interactions, the central goal will be to investigate magnetic systems, in particular to create anti-ferromagnetic many-body states. The Cs sample, for which we routinely achieve ultralow temperatures and extremely pure Bose-Einstein condensates, would serve as a perfect coolant and probe. With KCs, which is non-reactive and hence stable, we will enter a qualitatively new regime of fermionic systems with long-range dipolar interactions.