The goal of this chapter is to derive the formula for the electromagnetic HamiltonianHamiltonianelectromagnetic. This function describes the energy of interaction of a charged particle with the electromagnetic field. We start by reformulating Newton’s[aut]Newton, Isaac second lawNewton’s second law of motion in terms of Hamilton’s dynamical equations. The electric and magnetic fields are expressed in terms of the scalar potential and the vector potential, respectively, which were introduced in Chap. 8 . Upon including these potentials in the equations of motion, we are led to the Lagrange function, which is the difference between the kinetic and potential energies. From Lagrange’s function, we derive the Hamiltonian functionHamiltonianfunction which determines the total energy. This Hamiltonian will serve as the basis for our subsequent calculation of the quantum effects associated with the interaction of a charged particle with an electromagnetic field.