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We have undertaken a deep, wide-field HI imaging survey of M31, reaching amaximum resolution of about 50 pc and 2 km/s across a 95x48 kpc region. The HImass and brightness sensitivity at 100 pc resolution for a 25 km/s widespectral feature is 1500 M_Sun and 0.28 K. Our study reveals ubiquitous HIself-opacity features, discernible in the first instance as filamentary localminima in images of the peak HI brightness temperature. Local minima areorganized into complexes of more than kpc length and are particularlyassociated with the leading edge of spiral arm features. Just as in the Galaxy,there is only patchy correspondence of self-opaque features with CO(1-0)emission. Localized opacity corrections to the column density exceed an orderof magnitude in many cases and add globally to a 30% increase in the atomic gasmass over that inferred from the integrated brightness under the usualassumption of negligible self-opacity. Opaque atomic gas first increases from20 to 60 K in spin temperature with radius to 12 kpc but then declines again to20 K beyond 25 kpc. We have extended the resolved star formation law down tophysical scales more than an order of magnitude smaller in area and mass thanhas been possible previously. The relation between total-gas-mass- andstar-formation-rate-density is significantly tighter than that withmolecular-mass and is fully consistent in both slope and normalization with thepower law index of 1.56 found in the molecule-dominated disk of M51 at 500 pcresolution. Below a gas-mass-density of about 5 M_Sun/pc^2, there is adown-turn in star-formation-rate-density which may represent a real localthreshold for massive star formation at a cloud mass of about 5x10^4 M_Sun.

A Wide-field High Resolution HI Mosaic of Messier 31: I. Opaque Atomic Gas and Star Formation Rate Density