The book describes the current state of the theory of dynamical symmetry and the method of coherent states - new directions in theoretical physics. developed over the past decade in connection with the problems of quantum optics, Superfluidity, the Theory of Magnetism and the Fundamental Questions of Quantum Mechanics. Symmetries and coherent states are based on a single approach, using the presence of an arbitrary N-dimensional dynamical system 2N motion integrals corresponding to the starting point of the trajectory in the phase space of the system. Dynamical symmetries are considered for both relativistic systems described by means of relativistic equations with internal variables, and for quantum mechanical systems described by Schrdinger and Dirac equations. Methods of the theory of representations of the dynamical symplectic group and coherent states detail the properties of nonstationary systems described by the Hamiltonian, which is an arbitrary quadratic form of coordinate and momentum operators. Important particular cases of such systems have been analyzed, for example, a range of quasi-energies has been built in the case of the periodic dependence of the Hamiltonian on time, and the motion and radiation of charge in external non-stationary electric and magnetic fields have been studied.