  There is a review of the main mathematical properties of system described by
singular Lagrangians and requiring Dirac-Bergmann theory of constraints at the
Hamiltonian level. The following aspects are discussed:
  i) the connection of the rank and eigenvalues of the Hessian matrix in the
Euler-Lagrange equations with the chains of first and second class constraints;
  ii) the connection of the Noether identities of the second Noether theorem
with the Hamiltonian constraints;
  iii) the Shanmugadhasan canonical transformation for the identification of
the gauge variables and for the search of the Dirac observables, i.e. the
quantities invariant under Hamiltonian gauge transformations.
  Review paper for a chapter of a future book.
