  There is currently a great deal of interest in the theoretical and practical
possibility of cloaking objects from the observation by electromagnetic waves.
The basic idea of these invisibility devices \cite{glu1, glu2, le},\cite{pss1}
is to use anisotropic {\it transformation media} whose permittivity and
permeability $\var^{\lambda\nu}, \mu^{\lambda\nu}$, are obtained from the ones,
$\var_0^{\lambda\nu}, \mu^{\lambda\nu}_0$, of isotropic media, by singular
transformations of coordinates. In this paper we study electromagnetic cloaking
in the time-domain using the formalism of time-dependent scattering theory.
This formalism allows us to settle in an unambiguous way the mathematical
problems posed by the singularities of the inverse of the permittivity and the
permeability of the {\it transformation media} on the boundary of the cloaked
objects. We write Maxwell's equations in Schr\"odinger form with the
electromagnetic propagator playing the role of the Hamiltonian. We prove that
the electromagnetic propagator outside of the cloaked objects is essentially
self-adjoint. Moreover, the unique self-adjoint extension is unitarily
equivalent to the electromagnetic propagator in the medium
$\var_0^{\lambda\nu}, \mu^{\lambda\nu}_0$. Using this fact, and since the
coordinate transformation is the identity outside of a ball, we prove that the
scattering operator is the identity. Our results give a rigorous proof that the
construction of \cite{glu1, glu2, le}, \cite{pss1} perfectly cloaks passive and
active devices from observation by electromagnetic waves. Furthermore, we prove
cloaking for general anisotropic materials. In particular, our results prove
that it is possible to cloak objects inside general crystals.
