This paper presents the Hubble Ultra Deep Field (HUDF), a one million second exposure of an 11 square minute-of-arc region in the southern sky with the Hubble Space Telescope. The exposure time was divided among four filters, F435W (B435), F606W (V606), F775W (i775), and F850LP (z850), to give approximately uniform limiting magnitudes mAB~29 for point sources. The image contains at least 10,000 objects presented here as a catalog. Few if any galaxies at redshifts greater than ~4 resemble present day spiral or elliptical galaxies. Using the Lyman break dropout method, we find 504 B-dropouts, 204 V-dropouts, and 54 i-dropouts. Using these samples that are at different redshifts but derived from the same data, we find no evidence for a change in the characteristic luminosity of galaxies but some evidence for a decrease in their number densities between redshifts of 4 and 7. The ultraviolet luminosity density of these samples is dominated by galaxies fainter than the characteristic luminosity, and the HUDF reveals considerably more luminosity than shallower surveys. The apparent ultraviolet luminosity density of galaxies appears to decrease from redshifts of a few to redshifts greater than 6. The highest redshift samples show that star formation was already vigorous at the earliest epochs that galaxies have been observed, less than one billion years after the Big Bang.

44 pages, 18 figures, to appear in the Astronomical Journal October 2006