This chapter discusses the peculiarities of Maxwell’s equations, as well as some methods of solving them and some general consequences of them, for the case of gyrotropic media. It defines a gyrotropic medium as having nonsymmetric tensor parameters. The Landau–Lifshitz equation of motion, as well as the expressions for the tensor components, which are obtained by solving this equation, can be regarded as material equations for such substances. Waves with circular polarization pass through and reflect from the interfaces of different media without change of the polarization, and the complex amplitudes of the reflected and transmitted waves are easily found from the boundary conditions. The perturbation method is effective in calculating the quantities that are functionals of the electromagnetic field, such as eigenfrequencies of resonators or propagation constants of waveguides. The perturbation formulae for these quantities can be deduced from general quadratic relations, which can be called perturbation lemmas.