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The moon always faces the Earth and never turns with her back. Such "politeness" is due to the resonance. Therefore, we may truly consider that the resonance is something that can be associated with a course of an exact clock with a quartz crystal. However, Pluto, although until recently it was regarded as a planet, has an unpredictable orbit because of the same resonance. Rephrasing, this only means that before, people have been inclined to notice only to a laminar fume emanating from the incense stick and closed our eyes to the curls of the vortices, into which this stream very soon would be turned. This book avoids discussion of whether the resonance is that "demon" which manages the order. The goal is much more modest: along with a lot of relevant examples, to find such a strict mathematical definition of the resonance, which could serve as the essential tool in applied research of practicing physical engineers.