Advances in Microwaves, Volume 1 is a collection of papers dealing with the design and fabrication of a two-mile accelerator, optical waveguides, and directional couplers. One paper describes the design and fabrication of the disk-loaded wave guide, which serves as the accelerating structure, of the Stanford two-mile accelerator. Another paper discusses the basic principles of guided propagation, particularly the properties of the confocal lens systems or the "beam guide" variants. One paper describes the main types of directional couplers (namely, waveguide directional couplers, TEM-Mode directional couplers) to help scientists and researchers determine a particular design. Some papers discuss singular integral equations to solve waveguide problems, the application of Lie algebraic theory to microwave networks, and partially filled waveguides and surface waveguides of rectangular cross section. One paper explains the application of the singular integral equation method to rectangular waveguides, including the infinite parallel plate configuration. Another paper cites the exponentially tapered transmission line as an example to show the application of Lie algebras in solving problems related to the microwave field. The collection is suitable for people in the field of applied mathematics, nuclear physics, quantum mechanics, and applied physics.