  The electron shear viscosity due to Coulomb scattering of degenerate
electrons by atomic nuclei throughout a magnetized neutron star crust is
calculated. The theory is based on the shear viscosity coefficient calculated
neglecting magnetic fields but taking into account gaseous, liquid and solid
states of atomic nuclei, multiphonon scattering processes, and finite sizes of
the nuclei albeit neglecting the effects of electron band structure. The
effects of strong magnetic fields are included in the relaxation time
approximation with the effective electron relaxation time taken from the
field-free theory. The viscosity in a magnetized matter is described by five
shear viscosity coefficients. They are calculated and their dependence on the
magnetic field and other parameters of dense matter is analyzed. Possible
applications and open problems are outlined.
