[en] The cosmological evolution and the X-ray luminosity function of X-ray selected active galactic nuclei (AGNs) are derived and discussed.The sample used consists of 31 AGNs extracted from a fully identified sample of X-ray sources from the Einstein Observatory Medium Sensitivity Survey and is therefore exclusively defined by its X-ray properties. The distribution in space is found to be strongly nonuniform. The amount of cosmological evolution required by the X-ray data is derived in the framework of pure luminosity evolution and is found to be smaller than the amount determined from optically selected samples. The X-ray luminosity function is derived. It can be satisfactorily represented by a single power law only over a limited range of absolute luminosities. Evidence that the luminosity function flattens at low luminosity or steepens at high luminosity, or both, is presented and discussed