This book is an introduction to contemporary plasma physics that discusses the most relevant recent advances in the field and covers a careful choice of applications to various branches of astrophysics and space science. The purpose of the book is to allow the student to master the basic concepts of plasma physics and to bring him or her up to date in a number of relevant areas of current research. Topics covered include orbit theory, kinetic theory, fluid models, magnetohydrodynamics, MHD turbulence, instabilities, discontinuities, and magnetic reconnection. Some prior knowledge of classical physics is required, in particular fluid mechanics, statistical physics, and electrodynamics. The mathematical developments are self-contained and explicitly detailed in the text. A number of exercises are provided at the end of each chapter, together with suggestions and solutions.