  We detail how microlensing internal to M31 could be used to test whether a
large fraction of the matter in spiral galaxy haloes is composed of dark
objects with masses comparable to those of stars, and in the process show how
the microlensing matter is distributed in space and as a function of mass. A
survey of small fields in M31 has revealed several such candidate microlensing
events, at roughly the predicted rate. We discuss what efforts have been
required to further verify the microlensing nature of these events. We show how
halo lensing optical depth varies over the face of M31 depending on the shape
of the microlensing halo, and show how this shape could be determined in
representative results from a simulated survey in which roughly one-half square
degree is imaged for six hours every three nights on a two-meter telescope, in
1-arcsec seeing. After two or three seasons of such observation, the flattening
and core radius of the microlensing halo can be measured to an interesting
level of accuracy.
