This chapter provides an introduction to the analytical aspects of the wave diffraction in periodic anisotropic multilayers required for an efficient use of numerical procedures. The analysis can be generalized to laterally structure periodic multilayer systems. The approach finds applications in the design of various frequency selective elements including photonic crystals, in the spectroscopic ellipsometry for modelling surface roughness, and in-depth profiles. It forms the basis for the solution of inverse problem in the scatterometry of periodic nanostructures including semiconductor chips; liquid crystal structures; optic, magnetic, and magnetooptic recording disks; etc. The Rokushima formalism avoids the use of secondary parameters introduced in the classical optics of non-absorbing crystals, e.g., optical axes, ordinary and extraordinary rays, etc. The subject forms the basis for the solution of inverse problems employed, e. g., in scatterometry, also called optical critical dimension measurement method.