  We present the most up-to-date X-ray luminosity function (XLF) and absorption
function of Active Galactic Nuclei (AGNs) over the redshift range from 0 to 5,
utilizing the largest, highly complete sample ever available obtained from
surveys performed with Swift/BAT, MAXI, ASCA, XMM-Newton, Chandra, and ROSAT.
The combined sample, including that of the Subaru/XMM-Newton Deep Survey,
consists of 4039 detections in the soft (0.5--2 keV) and/or hard ($>2$ keV)
band. We utilize a maximum likelihood method to reproduce the count-rate versus
redshift distribution for each survey, by taking into account the evolution of
the absorbed fraction, the contribution from Compton-thick (CTK) AGNs, and
broad band spectra of AGNs including reflection components from tori based on
the luminosity and redshift dependent unified scheme. We find that the shape of
the XLF at $z \sim 1-3$ is significantly different from that in the local
universe, for which the luminosity dependent density evolution model gives much
better description than the luminosity and density evolution model. These
results establish the standard population synthesis model of the X-Ray
Background (XRB), which well reproduces the source counts, the observed
fractions of CTK AGNs, and the spectrum of the hard XRB. The number ratio of
CTK AGNs to the absorbed Compton-thin (CTN) AGNs is constrained to be
$\approx$0.5--1.6 to produce the 20--50 keV XRB intensity within present
uncertainties, by assuming that they follow the same evolution as CTN AGNs. The
growth history of supermassive black holes is discussed based on the new AGN
bolometric luminosity function.
