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We describe the MgII Absorber-Galaxy Catalog, MAGIICAT, a compilation of 182 spectroscopically identified intermediate redshift (0.07 < z < 1.1) galaxies with measurements of MgII 2796, 2803 absorption from their circumgalactic medium within projected distances of 200 kpc from background quasars. In this work, we present "isolated" galaxies, which are defined as having no spectroscopically identified galaxy within a projected distance of 100 kpc and a line of sight velocity separation of 500 km/s. We standardized all galaxy properties to the Lambda CDM cosmology and galaxy luminosities, absolute magnitudes, and rest-frame colors to the B- and K-band on the AB system. We present galaxy properties and rest-frame MgII equivalent width, Wr(2796), versus galaxy redshift. The well-known anti-correlation between Wr(2796) and quasar-galaxy impact parameter, D, is significant to the 8 sigma level. The mean color of MAGIICAT galaxies is consistent with an Sbc galaxy for all redshifts. We also present B- and K-band luminosity functions for different Wr(2796) and redshift subsamples: "weak absorbing" [Wr(2796) < 0.3 Ang], "strong absorbing" [Wr(2796) > 0.3 Ang], low redshift (z < zmed), and high redshift (z > zmed), where zmed = 0.359 is the median galaxy redshift. Rest-frame color B-K correlates with M_K at the 8 sigma level for the whole sample but is driven by the strong absorbing, high redshift subsample (6 sigma). Using M_K as a proxy for stellar mass and examining the luminosity functions, we infer that in lower stellar mass galaxies, MgII absorption is preferentially detected in blue galaxies and the absorption is more likely to be weak.