IRAS flux densities, redshifts, and infrared luminosities are reported for all sources identified in the IRAS Revised Bright Galaxy Sample (RBGS), a complete flux-limited survey of all extragalactic objects with total 60 micron flux density greater than 5.24 Jy, covering the entire sky surveyed by IRAS at Galactic latitude |b| > 5 degrees. The RBGS includes 629 objects, with a median (mean) sample redshift of 0.0082 (0.0126) and a maximum redshift of 0.0876. The RBGS supersedes the previous two-part IRAS Bright Galaxy Samples, which were compiled before the final (Pass 3) calibration of the IRAS Level 1 Archive in May 1990. The RBGS also makes use of more accurate and consistent automated methods to measure the flux of objects with extended emission. Basic properties of the RBGS sources are summarized, including estimated total infrared luminosities, as well as updates to cross-identifications with sources from optical galaxy catalogs established using the NASA/IPAC Extragalactic Database (NED). In addition, an atlas of images from the Digitized Sky Survey with overlays of the IRAS position uncertainty ellipse and annotated scale bars is provided for ease in visualizing the optical morphology in context with the angular and metric size of each object. The revised bolometric infrared luminosity function, phi(L_ir), for infrared bright galaxies in the local Universe remains best fit by a double power law, phi(L_ir) ~ L_ir^alpha, with alpha = -0.6 (+/- 0.1), and alpha = -2.2 (+/- 0.1) below and above the characteristic infrared luminosity L_ir ~ 10^{10.5} L_solar, respectively. (Abridged)
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