This book provides the latest achievements and original research work in physics of combustion processes and application of the methods developed in combustion physics for astrophysical problems of stars burning, supernovae explosions and a confined thermonuclear fusion. All the materials in the book are presented in a concise and easily accessible way, but at the same time provides a deep physical inside in the phenomena considered. It is an effective theoretical course with the direct practical implications in engineering fields of engine's development, energy production, safety issues inherent to terrestrial combustion, as well as in thermonuclear combustion in the inertial fusion. This book is aimed at university students, Ph.D. students and engineers, as well as professionals in combustion, energy-related research, astrophysics and researchers in neighboring fields.