  The Lagrangian and Hamiltonian formulations of electromagnetism are reviewed
and the Maxwell equations are obtained from the Hamiltonian for a system of
many electric charges. It is shown that three of the equations which were
obtained from the Hamiltonian, namely the Lorentz force law and two Maxwell
equations, can be obtained as well from a set of postulated Poisson brackets.
It is shown how the results derived from these brackets can be used to
reconstruct the original Lagrangian for the theory aided by some reasoning
based on physical concepts.
