This book presents the main mathematical methods of description and general problems in the theory of linear waves in dispersive systems and media, including equilibrium and nonequilibrium waves. To show how the general theory can be applied in practice, the authors give a unified description of the waves in all important physical systems which are traditionally studied in the mechanics of continuous media, electrodynamics, plasma physics, electronics and physical kinetics. Consideration is also given to the interaction of waves in coupled systems, the propagation and evolution of localized wave perturbations, and the emission of waves from dispersive media under the action of external sources moving in a prescribed manner. A general theory of instabilities of linear systems is given, in which the criteria for absolute and convective instabilities are formulated and compared, and Green's functions for some nonequilibrium media are calculated. Special attention is paid to problems in the theory of linear electromagnetic waves in plasmas and plasma-like media. The book also contains a number of original results of the present-day wave theory that have thus far been published in scientific journals only.