Starting from the original Majoranas article of 1937, the see-saw mechanism is illustrated, first for one and later for three neutrino generations, and neutrinoless double beta decay is considered. Neutrino mixing and oscillations in three flavors are described. The Yukawa couplings to the Higgs field of quarks and leptons are considered, their transformation properties under the corresponding flavor groups are spelled out and the principle of Minimal Flavor Violation is illustrated, in connection with possible new physics beyond the Standard Theory. The idea that the Yukawa couplings may be the vacuum expectation value of some new fields is introduced and natural extrema of potentials which are invariant under quark and lepton flavor groups are characterized. A recent result indicating large mixing of almost degenerate neutrinos is derived from the heavy lepton invariance under flavor ${cal O}(3)$.
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