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We present a total of 4784 unique broad absorption line quasars from theSloan Digital Sky Survey Third Data Release. An automated algorithm was used tomatch a continuum to each quasar and to identify regions of flux at least 10%below the continuum over a velocity range of at least 1000 km/s in the CIV andMgII absorption regions. The model continuum was selected as the best-fit matchfrom a set of template quasar spectra binned in luminosity, emission linewidth, and redshift, with the power-law spectral index and amount of dustreddening as additional free parameters. We characterize our sample through thetraditional ``balnicity'' index and a revised absorption index, as well asthrough parameters such as the width, outflow velocity, fractional depth andnumber of troughs. From a sample of 16883 quasars at 1.7<z<4.38, we identify4386 (26.0%) quasars with broad CIV absorption, of which 1756 (10.4%) satisfytraditional selection criteria. From a sample of 34973 quasars at 0.5<z<2.15,we identify 457 (1.31%) quasars with broad MgII absorption, 191 (0.55%) ofwhich satisfy traditional selection criteria. We also provide a supplementarylist of 39 visually identified z>4.38 quasars with broad CIV absorption. Wefind that broad absorption line quasars may have broader emission lines onaverage than other quasars.Comment: 47 pages, 14 figures, accepted for publication in ApJS. The  electronic version of Table 4 is provided by email reques

A Catalog of Broad Absorption Line Quasars from the Sloan Digital Sky Survey Third Data Release