The emphasis will be put on the evidences of lunar core existence and on the necessity to take this fact into account in the lunar librations theory. Our goal is to show how the millisecond precision observations of lunar physical librations in the projects. We discuss geophysical parameters, geometrical and dynamic ellipticity of liquid core and viscose-elastic mantel of the multilayered Moon. The research results include the survey of internal structure of the Moon, tabulated values of geophysical parameters and geophysical profile of the Moon, including liquid lunar core, values of geometrical compression on the Moon’s surface, densities, as well as graphic representations of the received data. The new prospects for horizons of research and development of the Moon for the nearest decade will be opened.