  It is proven that in the lossless case the electrodynamics of a generic
inhomogeneous possibly bianisotropic and nonreciprocal system may be described
by an augmented state-vector whose time evolution is determined by a Hermitian
operator. As a consequence, it is shown that a generic electromagnetic field
distribution can be expanded into a complete set of normal modes that satisfy
generalized orthogonality relations. Importantly, the modal expansions in
dispersive systems are not unique because the electromagnetic degrees of
freedom span only part of the entire Hilbert space. The developed theory is
used to obtain a modal expansion of the system Green's function.
  Furthermore, it is highlighted that the Hermitian-type formulation of the
dispersive Maxwell's equations enables one to extend the powerful ideas of
topological photonics to a wide range of electromagnetic systems and to
characterize electromagnetic topological phases. In addition, we illustrate how
the developed formalism can be applied to quantum optics. We present a simple
procedure to quantize the electromagnetic field in a generic bianisotropic and
nonreciprocal cavity and derive the quantum correlations of the electromagnetic
fields.
