  We present a new catalog of HII regions in M31. The full disk of the galaxy
is covered in a 2.2 deg^2 mosaic of 10 fields observed with the Mosaic Camera
as part of the Local Group Galaxies survey. We used HIIphot, a code for
automated photometry of HII regions, to identify the regions and measure their
fluxes and sizes. A 10 {\sigma} detection level was used to exclude diffuse gas
fluctuations and star residuals after continuum subtraction. That selection
limit may result in missing some faint HII regions, but our catalog of 3691 HII
regions is still complete to a luminosity of LH{\alpha} = 10^34 erg/s. This is
five times fainter than the only previous CCD-based study which contained 967
objects in the NE half of M31. We determined the H{\alpha} luminosity function
(LF) by fitting a power law to luminosities larger than LH{\alpha} = 10^36.7
and determined a slope of 2.52\pm0.07. The in-arm and inter-arm LFs peak at
different luminosities but they have similar bright-end slopes. The inter- arm
regions are less populated (40% of total detected regions) and constitute only
14% of the total luminosity of LH{\alpha} = 5.6 /times 10^40 erg/s (after
extinction correction and considering 65% contribution from diffused ionized
gas). A star formation rate of 0.44 M\odot/yr was estimated from the H{\alpha}
total luminosity; this value is consistent with the determination from the
Spitzer 8 {\mu}m image. We removed all known and potential planetary nebulae,
yet we found a double peaked luminosity function. The inter-arm older
population suggests a starburst between 15 and 20 million years ago. This
result is in agreement with UV studies of the star formation history in M31
which found a star formation rate decrease in the recent past. We found a fair
spatial correlation between the HII regions and stellar clusters in selected
star forming regions. Most of the matched regions lie within the arm regions.
