We present a catalog of 224 broad absorption line quasars (BALQSOs) from the Sloan Digital Sky Survey's Early Data Release Quasar Catalog, including a relatively complete and homogeneous subsample of 131 BALQSOs. Since the identification of BALQSOs is subject to considerable systematic uncertainties, we attempt to create a complete sample of SDSS BALQSOs by combining the results of two automated selection algorithms and a by-eye classification scheme. One of these automated algorithms finds broad absorption line troughs by comparing with a composite quasar spectrum. We present the details of this algorithm and compare this method with one that uses a power-law fit to the continuum. The BALQSOs in our sample are further classified as high-ionization BALQSOs (HiBALs), low-ionization BALQSOs (LoBALs), and BALQSOs with excited iron absorption features (FeLoBALs); composite spectra of each type are presented. We further present a study of the properties of the BALQSOs in terms of the balnicity distribution, which rises with decreasing balnicity. This distribution of balnicities suggests that the fraction of quasars with intrinsic outflows may be significantly underestimated.