  We derive a general procedure for finding the electromagnetic normal modes in
layered structures. We apply this procedure to planar, spherical and
cylindrical structures. These normal modes are important in a variety of
applications. They are the only input needed in calculations of Casimir
interactions. We present explicit expression for the condition for modes and
Casimir energy for a large number of specific geometries. The layers are
allowed to be two-dimensional so graphene and graphene-like sheets as well as
two-dimensional electron gases can be handled within the formalism. Also forces
on atoms in layered structures are obtained. One side-result is the van der
Waals and Casimir-Polder interaction between two atoms.
