The famous Niels Bohr’s quantum–classical correspondence principle states that classical mechanics is a limiting case of the more general quantum mechanics. The quantum laws show up in two different, although not entirely independent ways: Discrete spectrum of finite motion; and Interference phenomena. The specific features of quantum dynamics of classically chaotic systems seem to be in striking contrast with those of genuine classical chaos. The plain two-dimensional areas with closed irregular borders called billiards are pet systems often used to illustrate characteristic features of the classical dynamical chaos. Response of an evolving in time quantum system to a weak external perturbation is of prime interest in the context of the problem of stability and reversibility of quantum motion. The chapter discusses the decoherence phenomenon in the electron transport through an open ballistic quantum dot as the problem is seen from the point of view of the general resonance-scattering theory.