The Faint Source Survey (FSS) is the definitive IRAS data set for faint point sources. The FSS was produced by point-source filtering the individual detector data streams and then coadding those data streams using a trimmed-average algorithm. The resulting images, or plates, give the best estimate from the IRAS survey data of the point source flux density at every surveyed point of the sky. The Faint Source Catalog (FSC) is a compilation of the sources extracted from the FSS plates that have met reasonable reliability requirements. Averaged over the whole catalog, the FSC is at least 98.5% reliable at 12 and 25 microns, and ~94% at 60 microns. For comparison, the IRAS Point Source Catalog (PSC) is > 99.997% reliable, but the sensitivity of the FSC exceeds that of the PSC by about a factor of 2.5. The FSC contains data for 173,044 point sources in unconfused regions with flux densities typically greater than 0.2 Jy at 12, 25, and 60 microns and greater than 1.0 Jy at 100 microns.