This table contains 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 ~20 Ms of effective exposure time over 331 fields, with an areal coverage of 13 deg², and 498 sources (the abstract of the reference paper states that there are 497 sources) detected in total over the 3-24 keV energy range. There are 276 sources with spectroscopic redshifts and classifications, largely resulting from the authors' extensive campaign of ground-based spectroscopic follow-up. The authors characterize the overall sample in terms of the X-ray, optical, and infrared source properties. The sample is primarily composed of active galactic nuclei (AGN), detected over a large range in redshift from z = 0.002 to 3.4 (median redshift z of 0.56), but also includes 16 spectroscopically confirmed Galactic sources. There is a large range in X-ray flux, from log (f_3-24keV) ~ -14 to -11 (in units of erg s^-1 cm^-2), and in rest-frame 10-40 keV luminosity, from log (L_10-40keV) ~ 39 to 46 (in units of erg s^-1), with a median of 44.1. Approximately 79% of the NuSTAR sources have lower-energy (<10 keV) X-ray counterparts from XMM-Newton, Chandra, and Swift XRT observations. The mid-infrared (MIR) analysis, using WISE all-sky survey data, shows that MIR AGN color selections miss a large fraction of the NuSTAR-selected AGN population, from ~15% at the highest luminosities (L_X > 10⁴⁴ erg s^-1) to ~80% at the lowest luminosities (L_X < 10⁴³ erg s^-1). The authors' optical spectroscopic analysis finds that the observed fraction of optically obscured AGN (i.e., the type 2 fraction) is F_Type 2_ = 53 (+14, -15) per cent, for a well-defined subset of the 8-24 keV selected sample. This is higher, albeit at a low significance level, than the type 2 fraction measured for redshift- and luminosity-matched AGNs selected by <10 keV X-ray missions. This table contains the Primary NuSTAR Serendipitous Source Catalog of 498 sources found using the source detection procedure described in Section 2.3 of the reference paper, and listed in Table 5 (op. cit.). Additional information on these Primary Catalog sources that the authors obtained using optical spectroscopy is available in Table 6 of the reference paper (q.v.). This table does not contain the 64 sources in the Secondary NuSTAR Serendipitous Source Catalog that were found using wavdetect and that are listed in Table 7 of the reference paper: this is available in the HEASARC database as a separate table, dubbed <a href="/W3Browse/nustar/nustarssc2.html">NUSTARSSC2</a>. This table was created by the HEASARC in July 2017 based on the machine-readable version of Table 5 from the reference paper, the Primary NuSTAR Serendipitous Source Catalog, that was obtsined from the ApJ web site. This is a service provided by NASA HEASARC .