Interacting fermions are a prime example of complex systems in quantum physics: the microscopic Schrödinger equation gives rise to a baffling variety of collective behavior, ranging from collective plasmon excitations in Fermi liquids to the emergence of anyonic quasiparticles in the quantum Hall effect. Despite these effects having been spectacularly confirmed in experiment (e.g., the 1998 Nobel Prize for Laughlin, Störmer, and Tsui “for their discovery of a new form of quantum fluid with fractionally charged excitations”), their rigorous understanding continues to pose major challenges to mathematicians. The last few years however have seen formidable progress of the mathematical theory, such as the development of approximate bosonization methods and rigorous renormalization group (multiscale) methods. The school aims to introduce mathematicians and physicists to renormalization group methods, and initiate the development of synergies with Bogoliubov-type methods.