We present a current catalog of 21 cm H i line sources extracted from the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA) survey over ∼2800 deg 2 of sky: the α.40 catalog. Covering 40% of the final survey area, the α.40 catalog contains 15,855 sources in the regions 07 h 30 m < R.A. < 16 h 30 m , +04 • < decl. < +16 • , and +24 • < decl. < +28 • and 22 h < R.A. < 03 h , +14 • < decl. < +16 • , and +24 • < decl. < + 32 • . Of those, 15,041 are certainly extragalactic, yielding a source

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... nsity of 5.3 galaxies per deg 2 , a factor of 29 improvement over the catalog extracted from the H i Parkes All-Sky Survey. In addition to the source centroid positions, H i line flux densities, recessional velocities, and line widths, the catalog includes the coordinates of the most probable optical counterpart of each H i line detection, and a separate compilation provides a cross-match to identifications given in the photometric and spectroscopic catalogs associated with the Sloan Digital Sky Survey Data Release 7. Fewer than 2% of the extragalactic H i line sources cannot be identified with a feasible optical counterpart; some of those may be rare OH megamasers at 0.16 < z < 0.25. A detailed analysis is presented of the completeness, width-dependent sensitivity function and bias inherent of the α.40 catalog. The impact of survey selection, distance errors, current volume coverage, and local large-scale structure on the derivation of the H i mass function is assessed. While α.40 does not yet provide a completely representative sampling of cosmological volume, derivations of the H i mass function using future data releases from ALFALFA will further improve both statistical and systematic uncertainties.