This text describes the development of astronomy in the Extreme Ultraviolet (EUV) wavelength range, from the first rocket-based experiments in the late 1960s through to the latest satellite missions. Discussions of the results from the most important space projects are followed by an analysis of the contributions made by EUV astronomy to the study of specific groups of astronomical objects. Within this framework, the book provides detailed material on the tools of EUV astronomy, dealing with the instrumentation, observational techniques, and modelling tools for the interpretation of data. Prospects for future EUV missions are discussed, and a catalogue of the known EUV sources is included. This timely book will be of great value to graduate students and researchers. It is the first to give a complete overview of Extreme Ultraviolet astronomy, and comes at the end of a major phase of discovery in the field.