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

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... l 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