We present the Texas Survey of discrete radio sources between -35.5deg and 71.5deg declination (B1950), which was carried out at 365MHz with the Texas Interferometer during 1974-1983. The Survey lists accurate positions with internal errors of about an arcsecond, flux densities which for strong point sources have internal errors of about 1% and total errors of about 5%, simple structure models and indications of spectrum and variability for 66841 sources. Results of comparisons with other data are presented, and show that the Survey is 90% complete at 0.4Jy and 80% complete at 0.25Jy, is nearly free from spurious sources, and has a lobeshift incidence which is reasonably described by quality flags associated with each source. Introduction: The University of Texas Radio Astronomy Observatory (UTRAO) has carried out, with the Texas Interferometer, a 365MHz survey of the sky from -35.5 to +71.5{deg} declination, which was intended to be complete to a flux density level of 0.25Jy, to provide positions with an accuracy of about 1arcsec in both coordinates, to give accurate flux densities and indication of source variability, and to give rough structure models for each source. The observations began in 1974 and were completed in 1983. A preliminary version of one declination strip was published (Douglas et al., 1980), and a number of intermediate versions of the survey have been privately circulated for various purposes pending completion of the final analysis and adjustment of the data.