  We present a comprehensive study of star-forming (SF) regions in the nearest
large spiral galaxy M31. We use GALEX far-UV (1344-1786 \AA, FUV) and near-UV
(1771-2831 \AA, NUV) imaging to detect young massive stars and trace the recent
star formation across the galaxy. The FUV and NUV flux measurements of the SF
regions, combined with ground-based data for estimating the reddening by
interstellar dust from the massive stars they contain, are used to derive their
ages and masses. The GALEX imaging, combining deep sensitivity and coverage of
the entire galaxy, provides a complete picture of the recent star formation in
M31 and its variation with environment throughout the galaxy. The FUV and NUV
measurements are sensitive to detect stellar populations younger than a few
hundred Myrs. We detected 894 SF regions, with size > 1600 pc^{2} above an
average FUV flux limit of ~ 26 ABmag arcsecond^{-2}, over the whole 26 kpc
galaxy disk. We derive the star-formation history of M31 within this time span.
The star formation rate (SFR) from the youngest UV sources (age < 10 Myr) is
comparable to that derived from H_{alpha}, as expected. We show the dependence
of the results on the assumed metallicity. When star formation detected from IR
measurements of the heated dust is added to the UV-measured star formation
(from the unobscured populations) in the recent few Myrs, we find the SFR has
slightly decreased in recent epochs, with a possible peak between 10 and 100
Myrs, and an average value of SFR ~ 0.6 or 0.7 M_{sun} yr^{-1} (for metallicity
Z=0.02 or 0.05 respectively) over the last 400 Myrs.
