Abstract
Nonzero neutrino masses would provide new, unique information on particle physics beyond the standard model. Neutrino flavor oscillations provide the most sensitive method for directly testing for small neutrino masses. When the oscillations occur in matter, a resonance can occur that dramatically enhances the flavor mixing and can lead to conversion from one neutrino flavor to another. This is an attractive solution to the long-standing "solar neutrino problem." The phenomenon of neutrino oscillations in matter is reviewed. Analytic descriptions of the neutrino flavor survival probability in matter are considered in detail. A discussion is given for applications of neutrino oscillations in matter for the sun, Earth, supernovae, and the early universe.
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