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.
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