This e-book is a short history of self-propagating high-temperature synthesis (SHS) of inorganic materials and substances. The author considers distinct features of the research work of the most active groups along with their important scientific and practical achievements. The main result of these efforts is the appearance a new field of knowledge on the boundary between combustion science and materials science. The book is written in an original manner which combines the description of the scientific results with interesting stories about various episodes accompanying development of significant fields of science. The book should be of interest to for SHS specialists and representative students and researchers of allied sciences (physical and inorganic chemistry, macroscopic kinetics, materials science and technology of inorganic materials, metallurgy, etc.).