This is the first monograph to describe the historical development of ideas concerning the plasmasphere by the pioneering researchers themselves. The plasmasphere is a cold thermal plasma cloud encircling the Earth, terminating abruptly at a radial distance of 30,000 km over a sharp discontinuity known as the plasmapause. The volume commences with an account of the difficulties met in USSR by Gringauz to publish his early discoveries from Soviet rocket measurements, and the contemporaneous breakthroughs by Carpenter in the USA from ground-based whistler measurements. The authors then update our picture of the plasmasphere by presenting experimental and observational results of the past three decades, and mathematical and physical theories proposed to explain its formation. The volume will be invaluable for researchers in space physics, and will also appeal to those interested in the history of science.