  We present new observational determinations of the evolution of the 2-10keV
X-ray luminosity function (XLF) of AGN. We utilise data from a number of
surveys including both the 2Ms Chandra Deep Fields and the AEGIS-X 200ks
survey, enabling accurate measurements of the evolution of the faint end of the
XLF. We combine direct, hard X-ray selection and spectroscopic follow-up or
photometric redshift estimates at z<1.2 with a rest-frame UV colour
pre-selection approach at higher redshifts to avoid biases associated with
catastrophic failure of the photometric redshifts. Only robust optical
counterparts to X-ray sources are considered using a likelihood ratio matching
technique. A Bayesian methodology is developed that considers redshift
probability distributions, incorporates selection functions for our high
redshift samples, and allows robust comparison of different evolutionary
models. We find that the XLF retains the same shape at all redshifts, but
undergoes strong luminosity evolution out to z~1, and an overall negative
density evolution with increasing redshift, which thus dominates the evolution
at earlier times. We do not find evidence that a Luminosity-Dependent Density
Evolution, and the associated flattening of the faint-end slope, is required to
describe the evolution of the XLF. We find significantly higher space densities
of low-luminosity, high-redshift AGN than in prior studies, and a smaller shift
in the peak of the number density to lower redshifts with decreasing
luminosity. The total luminosity density of AGN peaks at z=1.2+/-0.1, but there
is a mild decline to higher redshifts. We find >50% of black hole growth takes
place at z>1, with around half in Lx<10^44 erg/s AGN.
