Parity violating electron nucleus scattering is a clean and powerful tool f
or measuring the spatial distributions of neutrons in nuclei with unprecede
nted accuracy. Parity violation arises from the interference of electromagn
etic and weak neutral amplitudes, and the Z(0) of the standard model couple
s primarily to neutrons at low Q(2). The data can be interpreted with as mu
ch confidence as electromagnetic scattering. After briefly reviewing the pr
esent theoretical and experimental knowledge of neutron densities, we discu
ss possible parity violation measurements, their theoretical interpretation
, and applications. The experiments are feasible at existing facilities. We
show that theoretical corrections are either small or well understood, whi
ch makes the interpretation clean. The quantitative relationship to atomic
parity nonconservation observables is examined. and we show that the electr
on scattering asymmetries can be directly applied to atomic parity nonconse
rvation because the observables have approximately the same dependence on n
uclear shape.