  We present a total of 4784 unique broad absorption line quasars from the
Sloan Digital Sky Survey Third Data Release. An automated algorithm was used to
match 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 and
MgII absorption regions. The model continuum was selected as the best-fit match
from a set of template quasar spectra binned in luminosity, emission line
width, and redshift, with the power-law spectral index and amount of dust
reddening as additional free parameters. We characterize our sample through the
traditional ``balnicity'' index and a revised absorption index, as well as
through parameters such as the width, outflow velocity, fractional depth and
number of troughs. From a sample of 16883 quasars at 1.7<z<4.38, we identify
4386 (26.0%) quasars with broad CIV absorption, of which 1756 (10.4%) satisfy
traditional 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%) of
which satisfy traditional selection criteria. We also provide a supplementary
list of 39 visually identified z>4.38 quasars with broad CIV absorption. We
find that broad absorption line quasars may have broader emission lines on
average than other quasars.
