We present the third edition of the Sloan Digital Sky Survey (SDSS)Quasar Catalog. The catalog consists of the 46,420 objects in the SDSSThird Data Release that have luminosities larger than Mi=-22(in a cosmology with H0=70 km s-1Mpc-1, ΩM=0.3, andΩΛ=0.7), have at least one emission line withFWHM larger than 1000 km s-1 or are unambiguously broadabsorption line quasars, are fainter than i=15.0, and have highlyreliable redshifts. The area covered by the catalog is ~4188deg2. The quasar redshifts range from 0.08 to 5.41, with amedian value of 1.47; the high-redshift sample includes 520 quasars atredshifts greater than 4, of which 17 are at redshifts greater than 5.For each object the catalog presents positions accurate to better than0.2" rms per coordinate, five-band (ugriz) CCD-based photometry withtypical accuracy of 0.03 mag, and information on the morphology andselection method. The catalog also contains radio, near-infrared, andX-ray emission properties of the quasars, when available, from otherlarge-area surveys. The calibrated digital spectra cover the wavelengthregion 3800-9200 Å at a spectral resolution of ~=2000 the spectracan be retrieved from the public database using the information providedin the catalog. A total of 44,221 objects in the catalog were discoveredby the SDSS; 28,400 of the SDSS discoveries are reported here for thefirst time.