The book describes the relationship of spectra with the structure and symmetry of crystals, analyzed new methods of group-theoretic analysis of spectra of the first and second orders. Numerous examples of analysis of vibrational spectra of crystals, as well as perturbations of intramolecular vibrations (Davydov splitting) in the crystalline state (ion, ion-covalent, molecular, layered and chain crystals) are analyzed.