The Einstein Survey of Optically Selected Galaxies contains the results of a complete Einstein Imaging Proportional Counter (IPC) X-ray survey of optically-selected galaxies from the Shapley-Ames (S-A) Catalog (CDS Catalog <VII/112>), the Uppsala General Catalog (UGC, CDS Catalog <VII/26>) and the European Southern Observatory (ESO) Catalog (CDS Catalog <VII/115>). Well-defined optical criteria were used to select the galaxies, and X-ray fluxes were measured at the optically-defined positions. The result is a comprehensive list of X-ray detection and upper limit measurements for 1018 galaxies. Of these, 827 galaxies have either independent distance estimates or radial velocities. Associated optical, redshift, and distance data have been assembled for these galaxies, and their distances come from a combination of directly predicted distances and those predicted from the Faber-Burstein Great Attractor/Virgocentric infall model. The accuracy of the X-ray fluxes has been checked in three different ways; all are consistent with the derived X-ray fluxes being of <= 0.1 dex accuracy. In particular, there is agreement with previously published X-ray fluxes for galaxies in common with a 1991 study by Roberts et al. (1991ApJS...75..751R) and a 1992 study by Fabbiano et al. (1992ApJS...80..531F, also available at the HEASARC as a database table called EINGALCAT). This database was created at the HEASARC in May 2002 based on the ADC/CDS Catalog J/ApJS/111/163 and is derived from Tables 5, 6, 7, 12, 13, and 14 of the published paper. This is a service provided by NASA HEASARC .