Calcite (CaCO3) is a beautiful transparent mineral that readily cleaves into rhombohedra. Images viewed through a thin slice of a cleaved calcite crystal are split into two images, an effect known as double refraction, or birefringence. Birefringence is the most obvious manifestation of optical anisotropy in crystals. For any given wave normal, there are two light waves, transversely polarized in mutually perpendicular directions, traveling with different velocities, and consequently different refractive indices. Double refraction is caused by dielectric anisotropy. For transparent crystals like calcite, the magnetic susceptibility is small and the permeability μ ≌ μ0, the permeability of free space. In this class of materials the refractive index n = c/v = where c is the speed of light in vacuum, v the velocity of light in the crystal, and K is the dielectric constant measured at optical frequencies. Refractive indices of transparent materials lie between 1 and 3. Electromagnetic waves differ from acoustic waves in that there are, for a given wave normal, two waves rather than three. In the acoustic case there are, in general, two quasitransverse waves and a quasilongitudinal wave. Starting with Maxwell’s Equations and the material constitutive relations, the propagation of electromagnetic waves through transparent crystals are described in terms of the refractive indices, wave normals, and polarization directions.