In this chapter, we describe the propagation of X-rays in materials using Maxwell's equations and derive the basic equation for X-ray diffraction. Using the equation, we consider the refractive index and dispersion surface of X-rays from the dispersion relation, and then explain total internal reflection, the penetration depth of X-rays, reflectance, and X-ray standing waves (XSW). We also explain an X-ray waveguide that amplifies X-rays by confining XSW in an artificially produced multilayer film after deriving the reflectance from a thin single-layer film on a substrate material.