The recently initiated Arecibo Legacy Fast ALFA (ALFALFA) survey aims to map ∼7000 deg 2 of the high Galactic latitude sky visible from Arecibo, providing a H I line spectral database covering the redshift range between - 1600 and 18,000 km s -1 with ∼5 km s -1 resolution. Exploiting Arecibo's large collecting area and small beam size, ALFALFA is specifically designed to probe the faint end of the H I mass function in the local universe and will provide a census of H I in the surveyed sky area to faint flux limits, making it especially useful in synergy with wide-area surveys conducted at other wavelengths. ALFALFA will also provide the basis for studies of the dynamics of galaxies within the Local Supercluster and nearby superclusters, allow measurement of the H I diameter function, and enable a first wide-area blind search for local H I tidal features, H I absorbers at z < 0.06, and OH megamasers in the redshift range 0.16 < z < 0.25. Although completion of the survey will require some 5 years, public access to the ALFALFA data and data products will be provided in a timely manner, thus allowing its application for studies beyond those targeted by the ALFALFA collaboration. ALFALFA adopts a two-pass, minimum intrusion, drift scan observing technique that samples the same region of sky at two separate epochs to aid in the discrimination of cosmic signals from noise and terrestrial interference. Survey simulations, which take into account large-scale structure in the mass distribution and incorporate experience with the ALFA system gained from tests conducted during its commissioning phase, suggest that ALFALFA will detect on the order of 20,000 extragalactic H I line sources out to z ∼ 0.06, including several hundred with H I masses M HI < 10 7.5 M ⊙.