The Arecibo Galaxy Environment Survey (AGES) is one of several HI surveys utilising the new Arecibo L-band Feed Array (ALFA) fitted to the 305m radio telescope at Arecibo. The survey is specifically designed to investigate various galactic environments to higher sensitivity, higher velocity resolution and higher spatial resolution than previous fully sampled, 21 cm multibeam surveys. The emphasis is on making detailed observations of nearby objects although the large system bandwidth (100 MHz) will allow us to quantify the HI properties over a large instantaneous velocity range. In this paper we describe the survey and its goals and present the results from the precursor observations of a 5 degree x 1 degree region containing the nearby (~10 Mpc) NGC 628 group. We have detected all the group galaxies in the region including the low mass (M{HI}~10^7Mo) dwarf, dw0137+1541 (Briggs, 1986). The fluxes and velocities for these galaxies compare well with previously published data. There is no intra-group neutral gas detected down to a limiting column density of 2x10^{18}cm^{-2}. In addition to the group galaxies we have detected 22 galaxies beyond the NGC 628 group, 9 of which are previously uncatalogued.(Abridged)
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