  These lectures, presented at the International School of Physics ``Enrico
Fermi,'' deal with two major themes. The first is the remarkable story of the
solar neutrino problem, which (along with the atmospheric neutrino anomaly)
recently led to the discovery of massive neutrinos and neutrino oscillations,
physics beyond the standard model. I will describe the physics of the standard
solar model (SSM), the experimental program that was motivated by the
discrepancies between SSM predictions and the initial observations of Raymond
Davis, Jr., and his colleagues, and the recent results of SNO and
SuperKamiokande. These first lectures end with a description of what we have
learned about neutrino oscillations and the neutrino mass matrix, as well as
the open questions (neutrino charge conjugation properties, the absolute mass
scale, CP violation) that could ultimately impact our understanding of
baryogenesis, the origin of large-scale structure, and other topics in
cosmology and astrophysics. The second theme is the core-collapse supernova
mechanism and associated nucleosynthesis. This problem connects neutrino
physics, which controls much of the nuclear physics of the star, with the
long-term chemical evolution of our galaxy. In particular, the $r$-process,
which produces about half of the heavy elements, remains poorly understood,
despite important new constraints from studies of metal-poor halo stars. The
possible role of new neutrino properties on both the explosion mechanism and
nucleosynthesis is noted.
