This book explores the chemical processes of the radical polymerisation of different vinyl monomers, initiated vulcanisation of rubbers and curing of the polyester resins. Organic peroxides are mainly used as the initiators. Their main advantages are the thermal stability within the definite interval of temperatures and in different media, reactivity of the primary oxy – radicals in different reactions and their initiation efficiency and non – toxicity of the final decomposition products. The complexity of the above – said properties of the organic peroxides should be taken into account under solving the problem of their purposeful synthesis.