  We study the charged and neutral current weak interaction rates relevant for
the determination of neutrino opacities in dense matter found in supernovae and
neutron stars. We establish an efficient formalism for calculating differential
cross sections and mean free paths for interacting, asymmetric nuclear matter
at arbitrary degeneracy. The formalism is valid for both charged and neutral
current reactions. Strong interaction corrections are incorporated through the
in-medium single particle energies at the relevant density and temperature. The
effects of strong interactions on the weak interaction rates are investigated
using both potential and effective field-theoretical models of matter. We
investigate the relative importance of charged and neutral currents for
different astrophysical situations, and also examine the influence of
strangeness-bearing hyperons. Our findings show that the mean free paths are
significantly altered by the effects of strong interactions and the
multi-component nature of dense matter. The opacities are then discussed in the
context of the evolution of the core of a protoneutron star.
