The X-ray optics of synchrotron radiation beamlines are considered in this paper. The characteristics of synchrotron radiation which make it the premier source of light for studies in many regions of the electromagnetic spectrum are given. A chapter is devoted to the collimating, focusing and monochromating optics of two X-ray diffraction beamlines at the National Synchrotron Light Source. The beamlines are operated by the Naval Research Laboratory (NRL) and the Oak Ridge National Lab (ORNL). The major optical components of these beamlines are reviewed in regards to their function and their flexibility. A detailed analysis is performed on the NRL X-ray collimating mirror. The mirror is treated as an elastically bent beam. Deflection and slope error equations are developed which relate the shape of the bent mirror to its ideal surface. Visible light diffraction patterns collected from the mirror helped to establish operating conditions which provide good collimation. When the observed patterns are wed to the theoretical calculations, estimates of the average figure error are made. Finally, the effect of a highly collimated synchrotron beam on the reproducibility of the integrated intensities from polycrystalline materials is considered. The calculations show that except for the most fine grained materials, representative intensity measurements can only be made when the sample is permitted to move. / M.S.