"Functional Renormalization provides a bridge from fundamentalmicrophysical laws to macroscopic complexity and observations. Actinglike a ""theoretical microscope"" with variable resolution, it includes ina stepwise procedure the fluctuation effects which are responsible forthe emergence of complexity. It describes macroscopic phenomena that are notdirectly visible on the microscopic level as order, phase transitions andspontaneous symmetry breaking , and is flexible enough to accommodate thechange of effective degrees of freedom and associated effective laws. Thelaws of Nature become dependent on the length scale.We propose to develop non-perturbative flow equations into a precision toolfor the understanding of many body physics, that can be tested by experimentswith ultracold atoms.Fundamental questions as a formulation of quantum gravity as anon-perturbatively renormalizable quantum field theory, the emergence offundamental length scales or the origin of dark energy will be tackledwith this method.We also will address specific applications as the non-linear growth ofstructure in cosmology or the phase diagram of models for stronglycorrelated electrons."