The introduction contains an exposition of the basic principles of magnetic quantum acoutics and the possibility of its use to investigate the structure and the dynamics of solids. The distinguishing features of different double magnetoacoustic resonances (nuclear-nuclear, electron-nuclear, and electron-electron) are then considered. Results are presented of investigations of spin-phonon interactions, relaxation processes, and singularities of the structure in various classes of crystals, carried out with the aid of such resonances. This is followed by consideration of dynamic polarization of atomic nuclei with the aid of ultrasound. Particular attention is paid to the use of magnetoacoustic resonances for quantum amplification and generation of coherent phonons (acoustic masers) and for the development of quantum detectors for ultrasound.