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The Cosmic Neutrino Background (CNB) is a prediction of the standard cosmological model, but it has been never observed directly. Several methods of CNB direct detection have been proposed in the past and the most promising one is currently adopted to develop the PTOLEMY proposal. I will review the theory and the experimental methods of the CNB direct detection, describe the computation of the local density of relic neutrinos in the Milky Way and discuss what could be achieved by PTOLEMY.