This project will examine several important topics in ULF wave theory. These waves have periods that range from about 0.5 seconds to 10s of minutes. Five specific major topics will be addressed: (1) the damping of low azimuthal wave-number Alfven waves in the ionosphere, (2) frequency doubled compressional waves in the ring current, (3) giant pulsations, (4) the relationship of Pi2 pulsations to magnetospheric flow bursts and substorm onets, and (5) phase skipping in quasi-monochromatic wave. All these topics involve the interaction of waves and particles in either the magnetosphere of the ionosphere. Understanding these phenomena may lead to new ways of using ULF waves as a method of remote sensing of magnetopsheric phenomena.