The monograph is devoted to the problems of dynamic systems with gauge symmetry. The theory of dynamical systems with connections, the theory of systems with Grassman variables, the Hamiltonian continuous integrals method . are described in detail. A separate chapter is devoted to the problem of confinement. The monograph includes the results of research in recent years (non-trivial phase space, residual discrete calibration group, etc.) ). The monograph can serve as an introduction to the modern theory of calibration systems and the method of Hamiltonian continuum integrals. The book is designed for specialists in quantum field theory. It will also be useful for undergraduate and graduate students .