"During the last decade, cold atoms have become one of the best controlled quantum systems. The major achievements were of Bose-Einstein condensation and Fermi degeneracy in trapped gases. More recently, cold gases have entered the régime of strong interactions, with the most prominent breakthroughs beein the observation of superfluidity in a Fermi gas and the transition from a superfluid to a Mott insulator, arranging atoms site by site in a periodic optical lattice.Here we reach out for a new level of control. We will prepare a gas of Lithium atoms at very low temperature, at the focus of an ultra-high resolution microscope, allowing observations and manipulations of the gas at the scale of the atomic wavefunction using optical methods.We will first use this setup to probe directly and locally the correlations in a strongly interacting Fermi gas. By observing fluctuations in a small region of the cloud, we will observe the emergence of quantum correlations. These studies will be conducted first on three-dimensional gases, and then extended to two-dimensional gases, where a superfluid transition of the Kosterlitz-Thouless type is expected.We will then use our manipulation capabilities to implement a lattice on the atoms. A bundle of light beams, created by a programable light modulator will go through the microscope and create an array of microscopic traps. Due to the low mass of Lithium atoms, tunneling between these traps will occur at a high rate. In this site-by-site created lattice, we will prepare a Fermi gas with strong attractive interactions, and observe the emergence of charge-density waves, a state of matter analog to the celebrated Neel (antiferromagnetic) order."