Plasma Astrophysics is a translation from the Russian language; the topics discussed are based on lectures given by V.N. Tsytovich at several universities. The book describes the physics of the various phenomena and their mathematical formulation connected with plasma astrophysics. This book also explains the theory of the interaction of fast particles plasma, their radiation activities, as well as the plasma behavior when exposed to a very strong magnetic field. The text describes the nature of collective plasma processes and of plasma turbulence. One author explains the method of elementary excitation which he has developed. The book also discusses the sporadic radio-emission of the sun, galactic nuclei, radio-galaxies, quasars, and pulsars. The book explains that problems involving terrestrial plasma can be split into parts; in astrophysics, the approach is different. For example, particle acceleration is determined by turbulence spectra that in turn depends on the energy distribution of the accelerated particles. The authors also give theoretical results based on many calculations analysis of observational data: Tsytovich contributes new theoretical calculations. This book can prove helpful for nuclear scientists and researchers working with plasma physics or astro-physics.