Abstract:
New observations with atmospheric neutrinos from the underground experiments SuperKamiokande, Soudan 2, and MACRO, together with earlier results from Kamiokande and IMB, are reviewed. The most recent observations reconfirm aspects of atmospheric flavor content and of zenith angle distributions which appear anomalous in the context of null oscillations. The anomalous trends, exhibited with high statistics in both sub-GeV and multi-GeV data of the SuperKamiokande water Cherenkov experiment, occur also in event samples recorded by the tracking calorimeters. The data are well-described by disappearence of nu_mu flavor neutrinos arising in oscillations with dominant two-state mixing, for which there exists a parameter region allowed by all experiments. In a new analysis by SuperKamiokande, nu_mu -> nu_tau is favored over nu_mu -> nu_s as the dominant oscillation based upon absence of oscillation suppression from matter effects at high energies. The possibility for sub-dominant nu_mu -> nu_e oscillations in atmospheric neutrinos which arises with three-flavor mixing, is reviewed, and intriguing possibilities for amplification of this oscillation by terrestrial matter-induced resonances are discussed. Developments and future measurements which will enhance our knowledge of the atmospheric neutrino fluxes are briefly noted.

Abstract:
We consider a solution of the atmospheric neutrino problem based on oscillations of muon neutrinos to sterile neutrinos: $\nu_{\mu}$ $\leftrightarrow$ $\nu_s$. The zenith angle ($\Theta$) dependences of the neutrino and upward-going muon fluxes in presence of these oscillations are studied. The dependences have characteristic form with two dips: at $\cos \Theta = -0.6 \div -0.2$ and $\cos \Theta = -1.0 \div -0.8$. The latter dip is due to parametric resonance in oscillations of neutrinos which cross the core of the earth. A comparison of predictions with data from the MACRO, Baksan and Super-Kamiokande experiments is given.

Abstract:
Motivated by recent results from SuperKamiokande, we study both solar and atmospheric neutrino fluxes in the context of oscillations of the three known neutrinos. We aim at a global view which identifies the various possibilities, rather than attempting the most accurate determination of the parameters of each scenario. For solar neutrinos we emphasise the importance of performing a general analysis, independent of any particular solar model and we consider the possibility that any one of the techniques --- chlorine, gallium or water Cerenkov --- has a large unknown systematic error, so that its results should be discarded. The atmospheric neutrino anomaly is studied by paying special attention to the ratios of upward and downward going nu_e and nu_mu fluxes. Both anomalies can be described in a minimal scheme where the respective oscillation frequencies are widely separated or in non-minimal schemes with two comparable oscillation frequencies. We discuss explicit forms of neutrino mass matrices in which both atmospheric and solar neutrino fluxes are explained. In the minimal scheme we identify only two `zeroth order' textures that can result from unbroken symmetries. Finally we discuss experimental strategies for the determination of the various oscillation parameters.

Abstract:
We briefly review the current status of standard oscillations of atmospheric neutrinos in schemes with two, three, and four flavor mixing. It is shown that, although the pure \nu_\mu-->\nu_\tau channel provides an excellent 2\nu fit to the data, one cannot exclude, at present, the occurrence of additional subleading \nu_\mu-->\nu_e oscillations (3\nu schemes) or of sizable \nu_\mu-->\nu_s oscillations (4\nu schemes). It is also shown that the wide dynamical range of energy and pathlength probed by the Super-Kamiokande experiment puts severe constraints on nonstandard explanations of the atmospheric neutrino data, with a few notable exceptions.

Abstract:
Neutrinos can scatter electrons in water detectors through their magnetic moments and charge radii in addition to the charged and neutral currents channels. The recent solar neutrino charged current event rates announced by SNO with the earlier solar and atmospheric neutrino observations from Super-Kamiokande allows us to put upper bounds of $\mu <10^{-9} \mu_B$ on neutrino magnetic moments and $ < 10^{-31} cm^2$ on the neutrino charge radii. For the electron and muon neutrinos these bounds are comparable with existing bounds but for tau neutrinos these bounds are three orders of magnitude more stringent than earlier terrestrial bounds. These bounds are independent of any specific model of neutrino oscillations.

Abstract:
We present an exact analytic solution to the neutrino evolution equation in matter with periodic step-function density profile and discuss in detail the parametric resonance of neutrino oscillations that can occur in such a system. Solar and atmospheric neutrinos traversing the earth pass through layers of alternating density and can therefore experience parametric resonance of their oscillations. Atmospheric neutrinos can undergo parametrically enhanced oscillations in the earth when their trajectories deviate from the vertical by about $26^\circ - 32^\circ$. Solar neutrinos traversing the earth can experience a strong parametric resonance of their oscillations in a wide range of zenith angles. If the small mixing angle MSW effect is the solution of the solar neutrino problem, the oscillations of solar neutrinos crossing the core of the earth {\em must} undergo strong parametric resonance; this phenomenon should facilitate significantly the observation of the day-night effect in oscillations of solar neutrinos. If observed, the enhanced day-night effect for core crossing neutrinos would therefore confirm both the MSW solution of the solar neutrino problem and the parametric resonance of neutrino oscillations.

Abstract:
After some generalities on neutrino oscillations and on neutrinos, the recent experimental results presented by Soudan 2, MACRO and SuperKamiokande at the Neutrino'98 conference are summarized and discussed.

Abstract:
One possible feature of quantum gravity may be the violation of Lorentz invariance. In this paper we consider one particular manifestation of the violation of Lorentz invariance, namely modified dispersion relations for massive neutrinos. We show how such modified dispersion relations may affect atmospheric neutrino oscillations. We then consider how neutrino telescopes, such as ANTARES, may be able to place bounds on the magnitude of this type of Lorentz invariance violation.

Abstract:
We consider the ``standard'' spectrum of the active neutrinos (characterized by strong mass hierarchy and small mixing) with additional sterile neutrino, $\nu_s$. The sterile neutrino mixes strongly with the muon neutrino, so that $\nu_{\mu} \leftrightarrow \nu_s$ oscillations solve the atmospheric neutrino problem. We show that the parametric enhancement of the $\nu_{\mu} \leftrightarrow \nu_s$ oscillations occurs for the high energy atmospheric neutrinos which cross the core of the Earth. This can be relevant for the anomaly observed by the MACRO experiment. Solar neutrinos are converted both to $\nu_{\mu}$ and $\nu_s$. The heaviest neutrino ($\approx \nu_{\tau}$) may compose the hot dark matter of the Universe. Phenomenology of this scenario is elaborated and crucial experimental signatures are identified. We also discuss properties of the underlying neutrino mass matrix.

Abstract:
The energy of atmospheric neutrinos detected by MACRO was estimated using multiple coulomb scattering of upward throughgoing muons. This analysis allows a test of atmospheric neutrino oscillations, relying on the distortion of the muon energy distribution. These results have been combined with those coming from the upward throughgoing muon angular distribution only. Both analyses are independent of the neutrino flux normalization and provide strong evidence, above the 4 sigma level, in favour of neutrino oscillations.