  The lecture notes document the mathematical theory of microwave and optical
waveguides. We start with reviewing preliminary background from Maxwell's
equations. Then we discuss hollow waveguides, and inhomogeneously-filled
waveguides, coupling of waveguides and cavities, discontinuities in waveguides.
We will also cover optical waveguides such as optical fibers, as well as
microwave integrated circuits. We end by discussing introductory soliton
concepts. It is intended for graduate students who have had a first course in
graduate electromagnetic theory.
