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The method for searching the Dirac observables of a gauge theory with first- and second-class constraints based on the Shanmugadhasan canonical transformation is described. Then, for clarifying all the aspects of gauge theories there is a study of the Hessian matrix of singular Lagrangians, of the possible degenerate cases, of the equivalence of the second Noether theorem with Dirac–Bergmann theory of constraints, and of the properties of the constraints of field theories.