This book provides a thorough account of the current status of achievements made in the area of soft X-Ray laser source development and of the increasingly diverse applications being demonstrated using such radiation sources. There is significant effort worldwide to develop very bright, short duration radiation sources in the X-Ray spectral region - driven by the multitude of potential applications in all branches of science. This book contains updates on several different approaches for comparative purposes but concentrates on developments in the area of laser-produced plasmas, whereby transient population inversion and gain between ion states is pumped by optical lasers interacting with pre-formed plasmas. Topics covered will include Laser-driven XRLs, Collisional XRLs, Recombination XRLs, Transient Inversion Collisional XRLs, Optical Field Ionization XRLs, Alternative XRL, pumping schemes Theory and simulations of XRL gain media and beam properties High order harmonic sources of XUV radiation, Free-electron lasers and other accelerator based X-Ray sources, X-Ray Laser drives, X-Ray optics and instrumentation Spectroscopy, and other diagnostics of laser media Applications of XRLs.