This paper suggests an axiomatic approach to Maxwell’s equations. The basis of this approach is a
theorem formulated for two sets of functions localized in space and time. If each set satisfies a
continuity equation then the theorem provides an integral representation for each function. A
corollary of this theorem yields Maxwell’s equations with magnetic monopoles. It is pointed out that
the causality principle and the conservation of electric and magnetic charges are the most
fundamental physical axioms underlying these equations. Another application of the corollary yields
Maxwell’s equations in material media. The theorem is also formulated in the Minkowski space-time
and applied to obtain the covariant form of Maxwell’s equations with magnetic monopoles and the
covariant form of Maxwell’s equations in material media. The approach makes use of the
infinite-space Green function of the wave equation and is therefore suitable for an advanced course
in electrodynamics.