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"The book consists of four Chapters. Chapter 1 shortly describes main properties of space plasmas and primary CR, different types of CR interactions with space plasmas components Chapter 2 considers the problem of CR propagation in space plasmas described by the kinetic equation and different types of diffusion approximations ,Chapter 3 is devoted to CR non-linear effects in space plasmas caused by CR pressure and CR kinetic stream instabilities with the generation of Alfvèn turbulence In Chapter 4 different processes of CR acceleration in space plasmas are considered: the development of the Fermi statistical mechanism, acceleration in the turbulent plasma, Alfven mechanism of magnetic pumping, induction mechanisms, acceleration during magnetic collapse and compression, cumulative acceleration mechanism near the zero lines of a magnetic field, acceleration in shear flows, shock-wave diffusion (regular) acceleration. The book ends with a list providing more than 1,300 full references, a discussion on future developments and unsolved problems, as well as Object and Author indexes. "