X-ray astronomy critically depends on X-ray optics. The capability of an X-ray telescope is largely determined by the point-spread function (PSF) and the photon-collection area of its mirrors, the same as telescopes in other wavelength bands. Since an X-ray telescope must be operated above the atmosphere in space and that X-rays reflect only at grazing incidence, X-ray mirrors must be both lightweight and thin, both of which add significant technical and engineering challenge to making an X-ray telescope. In this paper we report our effort at NASA Goddard Space Flight Center (GSFC) of developing an approach to making an Xray mirror assembly that can be significantly better than the mirror assembly currently flying on the Chandra X-ray Observatory in each of the three aspects: PSF, effective area per unit mass, and production cost per unit effective area. Our approach is based on the precision polishing of mono-crystalline silicon to fabricate thin and lightweight X-ray mirrors of the highest figure quality and micro-roughness, therefore, having the potential of achieving diffraction-limited X-ray optics. When successfully developed, this approach will make implementable in the 2020s and 2030s many X-ray astronomical missions that are currently on the drawing board, including sounding rocket flights such as OGRE, Explorer class missions such as STAR-X and FORCE, Probe class missions such as AXIS, TAP, and HEX-P, as well as large missions such as Lynx.