  We investigate the cosmological evolution of the hard X-ray luminosity
function (HXLF) of Active Galactic Nuclei (AGN) in the 2-10 keV luminosity
range of 10^{41.5} - 10^{46.5} erg s^-1 as a function of redshift up to 3. From
a combination of surveys conducted at photon energies above 2 keV with HEAO1,
ASCA, and Chandra, we construct a highly complete (>96%) sample consisting of
247 AGNs over the wide flux range of 10^{-10} - 3.8*10^{-15} erg cm^-2 s^-1
(2-10 keV). For our purpose, we develop an extensive method of calculating the
intrinsic (before-absorption) HXLF and the absorption (N_H) function. This
utilizes the maximum likelihood method fully correcting for observational
biases with consideration of the X-ray spectrum of each source. We find that
(i) the fraction of X-ray absorbed AGNs decreases with the intrinsic luminosity
and (ii) the evolution of the HXLF of all AGNs (including both type-I and
type-II AGNs) is best described with a luminosity dependent density evolution
(LDDE) where the cutoff redshift increases with the luminosity. Our results
directly constrain the evolution of AGNs that produce a major part of the hard
X-ray background, thus solving its origin quantitatively. A combination of the
HXLF and the NH function enables us to construct a purely "observation based"
population synthesis model. We present basic consequences of this model, and
discuss the contribution of Compton-thick AGNs to the rest of the hard X-ray
background.
