[en] Classical dynamical system in the Euclidean phase space, specified with a (primary) Hamiltonian H₀(q,p) and a number of constraint functions φ_k(q,p) is described equivalently by means of a new Hamiltonian H(q,p) which is an invariant of the (closed) Poisson-bracket Lie algebra (H₀, φ_k). The quantization is straightforward; it is given by the Heisenberg commutation relations in the embedding space. Values of a number of (commuting) constraint operators are fixed by initial conditions, while H itself does not bear an information on specific eigen-values of the constraint operators. In general, the system states are not pure and must be described in terms of the density operator (or corresponding Wigner phase-space distribution). Systems with Bose and Fermi degrees of freedom (and constraints) can be treated universally. The time evolution of the system can be represented by means of the phase-space path integral. Simple examples provide with illustrations to the general scheme. (orig.)