to Coherent Extreme-Ultraviolet and Soft X-Ray Sources -- Short Survey of XUV Emission Mechanisms and Sources -- XUV Optics -- Coherent XUV Radiation Beams -- State of the Art and Prospect of X-Ray Lasers -- Beginnings -- General Features of X-Ray Lasers -- Propagation of XUV Laser Beams -- Saturated XUV Lasers -- Recombination Lasers -- Schemes for Future Soft X-Ray Lasers -- High Harmonic Generation -- Survey of the Theoretical Background -- General Characteristics of High-Order Harmonic Emission -- A Survey of Coherent XUV Sources Applications -- Time-Resolution About 100 Picoseconds -- Time-Resolution About One Picosecond -- Subfemtosecond Time-Resolution -- Future Prospects.

Extreme ultraviolet radiation, also referred to as soft X-rays or XUV, offers very special optical properties. The X-UV refractive index of matter is such that normal reflection cannot take place on polished surfaces whereas beam transmission through one micrometer of almost all materials reduces to zero. Therefore, it has long been a difficult task to imagine and to implement devices designed for complex optics experiments in this wavelength range. Thanks to new sources of coherent radiation - XUV-lasers and High Order Harmonics - the use of XUV radiation, for interferometry, holography, diffractive optics, non-linear radiation-matter interaction, time-resolved study of fast and ultrafast phenomena and many other applications, including medical sciences, is ubiquitous.