This book deals with microwave and optical transmission from the unique viewpoint of Maxwell's theory, and via the consistent theoretical framework of coupled modes (ideal modes, local modes and super modes). A feature of the book is its particular emphasis on the usefulness of the coupled mode theory. The author has carried out to the end the solution of a diversity of waveguide problems, such as curved waveguides, tapered waveguides, tolerances of imperfections for a microwave and optical transmission line, etc. Another feature reflected in this volume is its presentation of adequate background material required for understanding the theory, which often appears complicated and difficult in the literature. The book begins with phenomenological theories of coupled modes, with the intention to familiarize the reader in a simple way with the basic concepts relevant to a further development of the coupled mode theory. Solutions of the coupled mode equations with constant or variable coefficients and orthogonal expansions in waveguides, whose combination represents a complete solution of Maxwell's equations, are treated in mathematical detail, with sufficient physical description to elucidate the underlying principles.