In recent times the idea of cloaking has become very popular. After radar and sonar were discovered, problems of “visibility” reduction for physical bodies in air (by electromagnetic waves) or in water (by acoustical waves) have immediately become serious areas of research in physics. New technologies (sensors, actuators) of high spatial-temporal resolution, metamaterials and new computers with fast and accurate calculations, in combination with nontraditional versions of solutions to these boundary problems, have allowed physicists to obtain successful results in some cases. This e-book presents a rare attempt to understand the cloaking problem as a whole. The book should be useful for readers with a strong interest in contemporary problem solving approaches in the physics of waves.