We map the star formation history across M31 by fitting stellar evolution models to color-magnitude diagrams of each 83${times}$83$$ (0.3$times$1.4 kpc, deprojected) region of the PHAT survey outside of the innermost 6${times}$12$$ portion. We find that most of the star formation occurred prior to $sim$8 Gyr ago, followed by a relatively quiescent period until $sim$4 Gyr ago, a subsequent star formation episode about 2 Gyr ago and a return to relative quiescence. There appears to be little, if any, structure visible for populations with ages older than 2 Gyr, suggesting significant mixing since that epoch. Finally, assuming a Kroupa IMF from 0.1$-$100 M$_{odot}$, we find that the total amount of star formation over the past 14 Gyr in the area over which we have fit models is 5${times}$10$^{10}$ M$_{odot}$. Fitting the radial distribution of this star formation and assuming azimuthal symmetry, (1.5$pm$0.2)${times}$10$^{11}$ M$_{odot}$ of stars have formed in the M31 disk as a whole, (9$pm$2)${times}$10$^{10}$ M$_{odot}$ of which has likely survived to the present after accounting for evolutionary effects. This mass is about one fifth of the total dynamical mass of M31.
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