  We present an efficient method for computing lightcurves of an elliptical
source which is microlensed by a point mass. The amplification of an extended
source involves a two-dimensional integral over its surface brightness
distribution. We show that for a general surface brightness profile with an
elliptical symmetry, this integral can be reduced to one dimension. We derive
analytical results for the entire lightcurve in the limit of low (e.g.
planetary) mass lenses, and for the wings of all microlensing lightcurves in
general. In both cases, the lightcurve carries information about deviations of
the source from elliptical symmetry, e.g. due to spots. The method is used to
find the amplification of a circular red giant photosphere and an inclined
accretion disk. We demonstrate that microlensing of an emission line from a
disk can be used to infer the disk velocity structure and surface brightness
profile.
