The monograph poses issues related to the study of the non-stationarity of open star clusters (OSCs), starting with an analysis of the properties of the trajectories of individual stars to the study of collective motion of stars. A discussion of the dynamics of correlations and wave processes in such clusters is presented. The mechanisms of the dynamic evolution of OSCs, the gravitational instability of OSC nuclei, the spectra of frequencies and wavenumbers for oscillations of numerical models of OSCs, astrophysical applications of the results of studies of the dynamics of OSCs are considered. We address the monograph to academic researchers (astronomers and physicists) who are interested in astrophysics, the dynamics of stellar systems, and PhD and senior students of relevant specialities.