The NUMEN project aims at accessing experimentally driven information on Nuclear Matrix Elements (NME) involved in the half-life of the neutrinoless double beta decay (0 nu beta beta), by high-accuracy measurements of the cross sections of Heavy Ion (HI) induced Double Charge Exchange (DCE) reactions. Particular attention is given to the (O-18, Ne-18) and (Ne-20, O-20) reactions as tools for beta(+) beta(+) and beta(-) beta(-) decays, respectively. First evidence about the possibility to get quantitative information about NME from experiments is found for both kind of reactions. In the experiments, performed at INFN - Laboratory Nazionali del Sud (LNS) in Catania, the beams are accelerated by the Superconducting Cyclotron (CS) and the reaction products are detected by the MAGNEX magnetic spectrometer. The measured cross sections are challengingly low, limiting the present exploration to few selected isotopes of interest in the context of typically low-yield experimental runs. A major upgrade of the LNS facility is foreseen in order to increase the experimental yield of at least two orders of magnitude, thus making feasible a systematic study of all the cases of interest. Frontiers technologies are going to be developed, to this purpose, for the accelerator and the detection systems. In parallel, advanced theoretical models will be developed in order to extract the nuclear structure information from the measured cross sections.