GENIUS is a proposal for a large volume detector to search for rare events. An array of 40-400 'naked' HPGe detectors will be operated in a tank filled with ultra-pure liquid nitrogen. After a description of performed technical studies of detector operation in liquid nitrogen and of Monte Carlo simulations of expected background components, the potential of GENIUS for detecting WIMP dark matter, the neutrinoless double beta decay in 76-Ge and low-energy solar neutrinos is discussed
