Phenomenology of Neutrino Masses and Mixing

We discuss all possible schemes with four massive neutrinos inspired by the existing experimental indications in favour of neutrino mixing, namely the atmospheric, solar and LSND neutrino experiments. We argue that the scheme with a neutrino mass hierarchy is not compatible with the experimental results, likewise all other schemes with the masses of three neutrinos close together and the fourth mass separated by a gap needed to incorporate the LSND neutrino oscillation result. Only two schemes with two pairs of neutrinos with nearly degenerate masses separated by this gap of the order of 1 eV are in agreement with the results of all experiments, including those where no indications for neutrino oscillations have been found. We also point out the possible effect of big-bang nucleosynthesis on the 4-neutrino mixing matrix and its consequences for neutrino oscillations. Finally, we study predictions for neutrino oscillation experiments and $^3$H and $(\beta \beta)_{0\nu}$ decays, following from the two favoured neutrino mass spectra and mixing schemes. These predictions can be conceived as checks of the input used for arriving at the two favoured schemes