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The twentieth century has witnessed the transformation of astronomy from celestial mechanics to astrophysics. While optical telescopes may have presented a peek into the structure of the constituents of the universe, such as stars and galaxies, new windows of observation have revealed far more amorphous objects, from nebulae and sheets to filaments and voids, whose "violent" processes include flares, shocks, accretion disks and jets. In these processes, plasma is often the constituent matter-- as well as the medium through which the astrophysical setting becomes so violent. In this graduate level text, Tajima and Shibata offer a new synthesis starting where classic works on plasma physics left off. Beginning with a view of plasma astrophysics through fundamental processes of quasi-magnetostatic equilibria, quasi-hydrostatic equilibria, and non-equilibria, the authors go on to develop unique approaches to violent astrophysical plasmas-- as opposed to the more quiescent laboratory variety-- and their processes. The text continues with an exploration of the fundamental processes in hydrostatic, magnetostatic, and gravitational objects. The final chapter is devoted to a discussion of the applications of plasma astrophysics to cosmology, anticipating future developments in this exciting field.This text will be of enormous use to graduate-- and some advanced undergraduate-- students, as well as to physicists entering the field of plasma physics.