  We present a catalog of intervening MgII quasar absorption-line systems in
the redshift interval 0.36 <= z <= 2.28. The catalog was built from Sloan
Digital Sky Survey Data Release Four (SDSS DR4) quasar spectra. Currently, the
catalog contains > 17,000 measured MgII doublets. We also present data on the
~44,600 quasar spectra which were searched to construct the catalog, including
redshift and magnitude information, continuum-normalized spectra, and
corresponding arrays of redshift-dependent minimum rest equivalent widths
detectable at our confidence threshold. The catalog is available on the web. A
careful second search of 500 random spectra indicated that, for every 100
spectra searched, approximately one significant MgII system was accidentally
rejected. Current plans to expand the catalog beyond DR4 quasars are discussed.
Many MgII absorbers are known to be associated with galaxies. Therefore, the
combination of large size and well understood statistics makes this catalog
ideal for precision studies of the low-ionization and neutral gas regions
associated with galaxies at low to moderate redshift. An analysis of the
statistics of MgII absorbers using this catalog will be presented in a
subsequent paper.
