We present the results of a complete Einstein imaging proportional counter X-ray survey of optically-selected galaxies from the Shapley-Ames Catalog (Cat. <VII/112>), the Uppsala General Catalog (Cat. <VII/26>) and the European Southern Observatory Catalog (Cat. <VII/115>). Well-defined optical criteria are used to select the galaxies, and X-ray fluxes are 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 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).The data presented here will be used in further studies to characterize the X-ray output of galaxies of various morphological types and thus to enable the determination of the major sources contributing to the X-ray emission from galaxies.