X-ray surveys provide us with one of the least biased samples of Active Galactic Nuclei (AGNs) against obscuration. Here we present the most up-to-date AGN X-ray luminosity function (XLF) and absorption function over the redshift range from 0 to 5, using the largest, highly complete sample ever available obtained from surveys of various depth, depth, and energy bands. 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, contribution from Compton-thick AGNs, and AGN broad band X-ray spectra 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 (LDDE) model gives the best description. These results establish the standard population synthesis model of the X-Ray Background (XRB), which well reproduces the source counts in both soft and hard bands, the observed fractions of Compton-thick AGNs, and the spectrum of the XRB.