Neutrinos are one of the central ingredients in core-collapse supernova explosion and
their flavor oscillations in supernovae might affect many processes that occur in this
explosive environment. In this thesis, we study neutrino flavor oscillations in supernovae
both analytically and numerically. Analytically, we propose a simple model to
explain the flavor evolution history in the region of collective neutrino oscillations during
the neutronization neutrino burst and accretion phase of neutrino emission with
low matter density. We show that the formation of spectral splits induced by collective
neutrino oscillations can be well-understood using this model. We also apply this model
to discuss the flavor instability of neutrino oscillations that occurs in the cooling phase.
Numerically, we simulate neutrino flavor evolution history using the neutrino emission
data from a state-of-the-art 18 M⊙ supernova model. We discuss the time-dependence
of neutrino oscillations on neutrino emission characteristics and the supernova environment.
We then study the effect of neutrino oscillations on the nucleosynthesis that
occurs in the neutrino-driven wind. At last, we calculate the expected neutrino signals
in the IceCube detector and discuss the consequences.