We present a new catalog of H II regions in M31 . The full disk of the galaxy ( \sim 24 kpc from the galaxy center ) is covered in a 2.2 deg ^ { 2 } mosaic of 10 fields observed with the Mosaic Camera on the Mayall 4 m telescope as part of the Local Group Galaxies survey . We used HIIphot , a code for automated photometry of H II 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 H II regions , but our catalog of 3691 H II regions is still complete to a luminosity of L _ { H \alpha } = 10 ^ { 34 }  erg s ^ { -1 } . 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 L _ { H \alpha } = 10 ^ { 36.7 } and determined a slope of 2.52 \pm 0.07 . 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 L _ { H \alpha } = 5.6 \times 10 ^ { 40 }  erg s ^ { -1 } ( after extinction correction and considering 65 % contribution from diffused ionized gas ) . A star formation rate of 0.44 M _ { \odot }  yr ^ { -1 } 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 H II regions and stellar clusters in selected star forming regions . Most of the matched regions lie within the arm regions .