Abstract: We present the first full catalog and science results for the Nuclear Spectroscopic Telescope Array (NuSTAR) serendipitous survey. The catalog incorporates data taken during the first 40 months of NuSTAR operation, which provide approx. 20 Ms of effective exposure time over 331 fields, with an areal coverage of 13 deg2, and 497 sources detected in total over the 324 keV energy range. There are 276 sources with spectroscopic redshifts and classifications, largely resulting from our extensive c…