  We present calculations of magnetic field evolution by the Hall effect and
Ohmic decay in neutron star crusts. We first discuss when and for which neutron
stars the Hall effect is important relative to Ohmic decay. We compute the
evolution of an initial field distribution by Ohmic decay, and give approximate
analytic formulas for both the surface and interior fields as a function of
time. We then discuss the subsequent evolution by the Hall effect, giving
several examples which illustrate how the field configuration evolves. Hall
wave eigenfunctions are computed, including the effect of the large density
change across the crust. We estimate the response of the crust to the magnetic
stresses induced by Hall waves, and give a detailed discussion of the boundary
conditions at the solid-liquid interface. Finally, we discuss the implications
for the Hall cascade proposed by Goldreich & Reisenegger.
