We discuss the spectral analysis of a sample of 63 active galactic nuclei (AGN) detected above a limiting flux of S(8-24 keV) = 7 x 10^(-14) erg s^(-1) cm^(-2 in the multi-tiered NuSTAR extragalactic survey program. The sources span a redshift range z = 0-2.1 (median (z) = 0.58). The spectral analysis is performed over the broad 0.5–24 keV energy range, combining NuSTAR with Chandra and/or XMM-Newton data and employing empirical and physically motivated models. This constitutes the largest sample of AGN selected at 〉 10 keV to be homogeneously spectrally analyzed at these flux levels. We study the distribution of spectral parameters such as photon index, column density (N_H), reflection parameter (R), and 10–40 keV luminosity (L_X). Heavily obscured (log[N_H/cm^(-2] ≥ 23) and Compton-thick (CT; log[N_H/cm^(-2)] ≥ 24) AGN constitute ~25% (15–17 sources) and ~2–3% (1–2 sources) of the sample, respectively. The observed N_H distribution agrees fairly well with predictions of cosmic X-ray background population-synthesis models (CXBPSM). We estimate the intrinsic fraction of AGN as a function of N_H, accounting for the bias against obscured AGN in a flux-selected sample. The fraction of CT AGN relative to log[N_H/cm^(-2] = 20-24 AGN is poorly constrained, formally in the range 2–56% (90% upper limit of 66%). We derived a fraction (f_(abs)) of obscured AGN (log[N_H/cm^(-2]= 22-24) as a function of L_X in agreement with CXBPSM and previous z 〈 1 X-ray determinations. Furthermore, f_(abs) at z = 0.1-0.5 and log(L_x/erg s^(-1) ≈ 43.6-44.3 agrees with observational measurements/trends obtained over larger redshift intervals. We report a significant anti-correlation of R with L_X (confirmed by our companion paper on stacked spectra) with considerable scatter around the median R values
