  We present X-ray spectral analysis of XMM and Chandra observations in the
31.3 deg$^2$ Stripe-82X (S82X) field. Of the 6181 X-ray sources in this field,
we analyze a sample of 2937 active galactic nuclei (AGN) with solid redshifts
and sufficient counts determined by simulations. Our results show a population
with median values of spectral index $\Gamma=1.94_{-0.39}^{+0.31}$, column
density log$\,N_{\mathrm{H}}/\mathrm{cm}^{-2}=20.7_{-0.5}^{+1.2}$ and
intrinsic, de-absorbed, 2-10 keV luminosity
log$\,L_{\mathrm{X}}/\mathrm{erg\,s}^{-1}=44.0_{-1.0}^{+0.7}$, in the redshift
range 0-4. We derive the intrinsic fraction of AGN that are obscured
($22\leq\mathrm{log}\,N_{\mathrm{H}}/\mathrm{cm}^{-2}<24$), finding a
significant increase in the obscured AGN fraction with redshift and a decline
with increasing luminosity. The average obscured AGN fraction is $57\pm4\%$ for
log$\,L_{\mathrm{X}}/\mathrm{erg\,s}^{-1}>43$. This work constrains the AGN
obscuration and spectral shape of the still uncertain high-luminosity and
high-redshift regimes (log$\,L_{\mathrm{X}}/\mathrm{erg\,s}^{-1}>45.5$, $z>3$),
where the obscured AGN fraction rises to $64\pm12\%$. We report a luminosity
and density evolution of the X-ray luminosity function, with obscured AGN
dominating at all luminosities at $z>2$ and unobscured sources prevailing at
log$\,L_{\mathrm{X}}/\mathrm{erg\,s}^{-1}>45$ at lower redshifts. Our results
agree with evolutionary models in which the bulk of AGN activity is triggered
by gas-rich environments and in a downsizing scenario. Also, the black hole
accretion density (BHAD) is found to evolve similarly to the star formation
rate density, confirming the co-evolution between AGN and host-galaxy, but
suggesting different time scales in their growing history. The derived BHAD
evolution shows that Compton-thick AGN contribute to the accretion history of
AGN as much as all other AGN populations combined.

Astrophysics of Galaxies;High Energy Astrophysical Phenomena