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In the field of fundamental particle physics the neutrino has become more and more important in the last few years, since the discovery of its mass. In particular, the ultimate nature of the neutrino (if it is a Dirac or a Majorana particle) plays a crucial role not only in neutrino physics, but in the overall framework of fundamental particle interactions and in cosmology. The only way to disentangle its ultimate nature is to search for the so-called Neutrinoless Double Beta Decay (01ADBD). The goal of LUCIFER is to build a background-free 01ADBD experiment with a discovery potential better than the future, already approved, funded experiments. Although aiming at a discover, in the case of insufficient sensitivity the LUCIFER technique will be the demonstrator for a higher mass experiment able to probe the entire inverted hierarchy region of the neutrino mass and to start approaching the direct one. The idea of LUCIFER is to join the bolometric technique proposed for the CUORE experiment (one of the few 01ADBD experiments in construction world-wide) with the bolometric light detection technique used in cryogenic dark matter experiments. The bolometric technique allows an extremely good energy resolution while its combination with the scintillation detection offers an ultimate tool for background rejection. Preliminary tests on severa) 01ADBD detectors have clearly demonstrated the excellent background rejection capabilities that arise from the simultaneous, independent, double readout (heat + scintillation).