Introduction 323
1. Complex Dielectric Tensor [IMG align=ABSMIDDLE alt=$\epsilon$]eps[/IMG]_ij(ω, k) and Normal Waves in the Medium 328
a) The Tensor [IMG align=ABSMIDDLE alt=$\epsilon$]eps[/IMG]_ij(ω, k) and Its Properties 328
b) Normal Electromagnetic Waves in a Medium. Transverse and Longitudinal Waves. "Fictitious" Longitudinal Waves and "Polarization Waves" 331
c) Energy and Other Relations for Waves in an Anisotropic Medium 334
2. The Tensor [IMG align=ABSMIDDLE alt=$\epsilon$]eps[/IMG]_ij(ω, k) in Crystals 337
a) The Concept of the Tensor [IMG align=ABSMIDDLE alt=$\epsilon$]eps[/IMG]_ij(ω, k) for Crystals 337
b) The Case of Weak Spatial Dispersion (a/λ ≪ 1) 339
Cited Literature, Part I 345
3. Crystal optics with allowance for spatial dispersion, a) New wave near absorption line in gyrotropic crystals, b) New waves in non-gyrotropic crystals, c) Optical anisotropy of cubic crystals. Quadrupole absorption lines, d) Effect of mechanical stresses and external electric and magnetic fields, e) The problem of boundary conditions, f) Experimental investigations of effects of spatial dispersion in crystal optics. 4. Quantum mechanical calculation of the tensor [IMG align=ABSMIDDLE alt=$\epsilon$]eps[/IMG]_ij(ω, k). a) Quantum mechanical expression for [IMG align=ABSMIDDLE alt=$\epsilon$]eps[/IMG]_ij(ω, k). b) Mechanical excitons and the tensor [IMG align=ABSMIDDLE alt=$\epsilon$]eps[/IMG]_ij(ω, k) in molecular crystals and in the case of the classical oscillator model, c) Absorption mechanism and calculations. Concluding remarks. Cited literature, part II.