  An extensive study of the effects of correlations on both charged and neutral
current weak interaction rates in dense matter is performed. Both strong and
electromagnetic correlations are considered.The propagation of particle-hole
interactions in the medium plays an important role in determining the neutrino
mean free paths. The effects due to Pauli-Blocking and density, spin, and
isospin correlations in the medium significantly reduce the neutrino cross
sections. Due to the lack of experimental information at high density, these
correlations are necessarily model dependent. For example, spin correlations in
nonrelativistic models are found to lead to larger suppressions of neutrino
cross sections compared to those of relativistic models. This is due to the
tendency of the nonrelativistic models to develop spin instabilities.
Notwithstanding the above caveats, and the differences between nonrelativistic
and relativistic approaches such as the spin- and isospin-dependent
interactions and the nucleon effective masses, suppressions of order 2--3,
relative to the case in which correlations are ignored, are obtained. Neutrino
interactions in dense matter are especially important for supernova and early
neutron star evolution calculations. The effects of correlations for
protoneutron star evolution are calculated. Large effects on the internal
thermodynamic properties of protoneutron stars, such as the temperature, are
found. These translate into significant early enhancements in the emitted
neutrino energies and fluxes, especially after a few seconds. At late times,
beyond about 10 seconds, the emitted neutrino fluxes decrease more rapidly
compared to simulations without the effects of correlations, due to the more
rapid onset of neutrino transparency in the protoneutron star
