Theories of surface waves develop since the end of XIX century and many fundamental problems like existence, phase and group velocities, attenuation (quality factor), mode conversion, etc. have been, in part successfully, solved within the framework of such simple models as ideal fluids^ or linear elasticity. However, a sufficiently complete presentation of this subject, particularly for solids, is still missing in the literature. The sole exception is the book of I. A. Viktorov^ which contains an extensive discussion of fundamental properties of surface waves in homogeneous and stratified linear elastic solids with particular emphasis on contributions of Russian scientists. Unfortunately, the book has never been translated to English and its Russian version is also hardly available. Practical applications of surface waves develop intensively since a much shorter period of time than theories even though the motivation of discoverers of surface waves such as Lord Rayleigh stems from their appearance in geophysics and seismology. Nowadays the growing interest in practical applications of surface waves stem from the following two main factors: surface waves are ideal for developing relatively cheap and convenient methods of nondestructive testing of various systems spanning from nanomaterials (e.g.

Near-Surface Site Characterization Using Surface Waves.- Surface Wave Testing for Geotechnical Characterization.- Surface Waves in Dissipative Media: Forward and Inverse Modelling.- Waves Propagation Modes: From Simple Systems to Layered Soils.- Elastic modelling of surface waves in single and multicomponent systems.- Modelling of surface waves in poroelastic saturated materials by means of a two component continuum.- Theory of Nonlinear Surface Waves and Solitons.- Experimental Soil Behaviour: its Testing by Waves and Engineering Applications.