  This paper details a description of the pattern of galaxy image distortion
over the entire sky caused by the gravitational lensing which is the result of
large scale inhomogeneities in our universe. We present a tensor spherical
harmonic formalism to describe this pattern, giving many useful formulae. This
is applied to density inhomogeneities, where we compute the angular power
spectrum of the shear pattern, as well as the noise properties due to finite
galaxy sampling and cosmic variance. We show that a detectable level of shear
is present for very nearby galaxies, $z\simlt0.2$. For such a shallow sample
much of the largest signal-to-noise comes from very large angular scales,
$\theta\simgt10^\circ$, although it is in the form of very small shear at a
level $\simlt10^{-3}$.
