  Type 2 quasars are luminous active galactic nuclei (AGN) whose central
regions are obscured by large amounts of gas and dust. In this paper, we
present a catalog of type 2 quasars from the Sloan Digital Sky Survey (SDSS),
selected based on their optical emission lines. The catalog contains 887
objects with redshifts z < 0.83; this is six times larger than the previous
version and is by far the largest sample of type 2 quasars in the literature.
We derive the [OIII]5008 luminosity function for 10^8.3 Lsun < L[OIII] < 10^10
Lsun (corresponding to intrinsic luminosities up to M[2400A]-28 mag or
bolometric luminosities up to 4x10^47 erg/sec). This luminosity function
provides strong lower limits to the actual space density of obscured quasars,
due to our selection criteria, the details of the spectroscopic target
selection, as well as other effects. We derive the equivalent luminosity
function for the complete sample of type 1 (unobscured) quasars; then, we
determine the ratio of type 2/type 1 quasar number densities. Our best data
constrain this ratio to be at least 1.5:1 for 10^8.3 Lsun < L[OIII] < 10^9.5
Lsun at z < 0.3, and at least 1.2:1 for L[OIII]=10^10 Lsun at 0.3 < z < 0.83.
Type 2 quasars are at least as abundant as type 1 quasars in the relatively
nearby Universe (z < 0.8) for the highest luminosities.
