Neutrino Properties Deduced from the Study of Lepton Number Violating Processes at Low and High Energies

There is nowadays a significant progress in understanding the neutrino properties. The results of the neutrino oscillation experiments have convincingly showed that neutrinos have mass and oscillate, in contradiction with the Standard Model (SM) assumptions, and these are the first evidences of beyond SM physics. However, fundamental properties of the neutrinos like their absolute mass, their character (are they Dirac or Majorana particles?), their mass hierarchy, the number of neutrino flavors, etc., still remain unknown. In this context there is an increased interest in the study of the lepton number violating (LNV) processes, since they could complete our understanding on the neutrino properties. Since recently, the neutrinoless double beta decay was considered the only process able to distinguish between Dirac or Majorana neutrinos and to give a hint on the absolute mass of the electron neutrino. At present, the increased luminosity of the LHC experiments makes feasible the search of LNV processes at high energy as well. In this lecture I will make a brief review on our present knowledge of the neutrino properties, on the present status of the double-beta decay studies and on the first attempts to search LNV processes at LHC.