Dirac brackets in constrained dynamics

An unified geometric description of various Dirac brackets for regular and singular lagrangians with holonomic or non-holonomic constraints is present ed. Such unified picture relies only on two simple physical arguments: "cla ssical complementarity principle" and "principle of deterministic evolution ". The appropriate geometrization of these principles allows to construct a recursive constraint algorithm that eventually produces a maximal final st ate manifold where a well defined dynamics exists, naturally equipped with a Dirac bracket such that the dynamics is hamiltonian with respect to it. A classification of constraints in first and second class as envisaged by Di rac emerges also naturally from this picture. The Dirac brackets constructe d show explicitly the existence of classical anomalies for such lagrangian theories since in general they do not verify Jacobi's identity. Such featur es are discussed using a variety of examples.