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Galaxy clusters discovered via the Sunyaev-Zel'dovich effect in the first 720 square degrees of the South Pole Telescope survey

We present a catalog of 224 galaxy cluster candidates, selected through their Sunyaev-Zel'dovich (SZ) effect signature in the first 720 deg2 of the South Pole Telescope (SPT) survey. This area was mapped with the SPT in the 2008 and 2009 austral winters to a depth of 18 uK-arcmin at 150 GHz; 550 deg2 of it was also mapped to 44 uK-arcmin at 95 GHz. Based on optical imaging of all candidates and near-infrared imaging of the majority of candidates, we have found optical and/or infrared counterparts for 158 clusters. Of these, 135 were first identified as clusters in SPT data, including 117 new discoveries reported in this work. This catalog triples the number of confirmed galaxy clusters discovered through the SZ effect. We report photometrically derived (and in some cases spectroscopic) redshifts for confirmed clusters and redshift lower limits for the remaining candidates. The catalog extends to high redshift with a median redshift of z = 0.55 and maximum redshift of z = 1.37. Based on simulations, we expect the catalog to be nearly 100% complete above M500 ~ 5e14 Msun h_{70}^-1 at z > 0.6. There are 121 candidates detected at signal-to-noise greater than five, at which the catalog purity is measured to be 95%. From this high-purity subsample, we exclude the z < 0.3 clusters and use the remaining 100 candidates to improve cosmological constraints following the method presented by Benson et al., 2011. Adding the cluster data to CMB+BAO+H0 data leads to a preference for non-zero neutrino masses while only slightly reducing the upper limit on the sum of neutrino masses to sum mnu < 0.38 eV (95% CL). For a spatially flat wCDM cosmological model, the addition of this catalog to the CMB+BAO+H0+SNe results yields sigma8=0.807+-0.027 and w = -1.010+-0.058, improving the constraints on these parameters by a factor of 1.4 and 1.3, respectively. [abbrev]