  Our knowledge of the neutrino sector of the Standard Model has recently
undergone a revolution. Deficits of the atmospheric muon neutrino flux and the
solar electron neutrino flux compared to their predicted values can be
understood in terms of neutrino oscillations and we can therefore infer that
neutrinos have non-degenerate masses. Additional but somewhat less secure
evidence for \bar\nu_\mu \to \bar\nu_e and \nu_\mu\to\nu_e oscillations has
been found in the LSND accelerator experiment. Because these experiments have
widely different L/E_\nu ranges (\approx 10 to 10^4 km/GeV for atmospheric,
\approx 10^{11} for solar, and \approx 1 for LSND), the mass-squared
differences required to explain the phenomena must be distinct. Given the
observations, an important next step is to deduce the pattern of neutrino
masses and mixings. Such studies depend on the number of neutrinos. The
invisible width of the Z-boson measured in LEP experiments gives N_\nu =
2.993\pm 0.011, consistent with the usual \nu_e, \nu_\mu and \nu_\tau "active"
neutrinos. But there may also be right-handed "sterile" neutrinos with no weak
interactions. Only the observation of oscillations of the active neutrinos to
sterile neutrinos can test for their existence. In the following, we first
discuss the atmospheric and solar neutrino data in a 3-neutrino framework and
then later generalize our considerations to include the LSND data with
oscillations of four neutrinos.
