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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 broadband 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 ∼ 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 ≈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. [ABSTRACT FROM AUTHOR]