In this monograph on surface waves propagating in media with lateral inhomogeneities, the author takes into account the rapid progress made in applying surface waves in many fields of physics and engineering science during the last two decades. The fundamentals of surface waves have been a well-founded part of wave theory for many years. However, the application is connected with various problems which cannot be solved using conventional theory alone, such as input and output of surface wave energy in communication engineering devices, low-loss transfer of energy in wave-guides, the investigation of the Earth's interior using seismic surface waves, etc. A crucial problem common to these fields is the question of the interaction of surface waves with discontinuities. The primary objective of this book is to treat this problem in detail by using a very simple model, the so-called impedance surface. Although there are many books devoted to the propagation of waves in disturbed media, there is no cross-disciplinary treatise for surface waves which also considers seismological aspects.