Preface It is a well-known fact that development of some key military programs during the last fifty years systematically provoked critical situations in different parts of the applied physics. This happened mainly in cases when the appetite of the military exceeded the possibility of the existing, at that time, levels of science and technologies. The paradox of the situation is that every time, researchers, trying to solve arisen applied problems, made ultimately a next important step in fundamental sciences. As a result, we obtained systematically various new applied-fundamental achievements, which, naturally, were not foreseen initially by any military technical tasks. We have a similar scenario in the case of the hierarchic electrodynamics and the theory of hierarchic oscillations and waves. It all began with ancient experiments with the powerful plasma-beam instability, which were accomplished in 1950s through the 1960s (the famous Thermonuclear Plasma fusion Program). Essentially multiharmonic wave processes were observed, which have been characterized by the generation of tens and even hundreds of plasma-wave harmonics with commensurable amplitudes (Chapters 13 and 14). At that time, however, the observed experimental physical picture did not get any satisfactory theoretical description. Especially difficult mathematical situation took place in cases when the amplitudes of higher harmonics exceeded the amplitudes of the lower ones-- Provided by publisher.