A general phenomenological theory of the optical properties of gyrotropic crystals, which also have anisotropy of dielectric or magnetic permeability and absorption, is presented .. The basis of the consideration is based on direct (uncoordinated) methods of tensor calculus, which allow to simplify to a large extent the solution of the most complex and intricate problems of crystal optics. The necessary mathematical apparatus in an accessible form is described in detail in the last chapter of the book .. Since the gyrotropic properties of crystals are closely related to the manifestations of conventional anisotropy, a detailed presentation of the covariant theory of the optical properties of non-gyrotropic crystals, including magnetic and absorb. is first given. Much attention is paid to boundary tasks, including passing through crystalline plates. The main part of the content of the book is the original results of the author and his employees. The book can be useful to a wide range of people interested in crystal optics and electromagnetic wave propagation in anisotropic environments, including students, graduate students, researchers and engineers. The mathematical apparatus described in it can also be used in solving other problems of crystal physics, for example, in the theory of the magnetic properties of crystals.