The book examines the fundamental problem of innovative complexity in the context of the latest achievements of modern theory of complex systems. The results of studies of the sources and factors of the emergence of innovative complexity, features of its dynamic growth and cyclical evolution, ways of passing crises and instabilities in the course of evolution are presented. Particular attention is paid to the consideration of modern information, cognitive and communication technologies, problems of consciousness and creativity, stimulation of creativity, production of scientific, cultural and social innovations. Possible applications of models of the birth and evolution of innovative complexity for the analysis and forecasting of the development of natural, technical, cognitive and social systems are shown. The book is of interest not only to academic researchers, but also to a wide range of design, education and management practitioners seeking to make effective decisions in the face of uncertainty and ambiguity of the future and ensure the safety and quality of functioning of complex systems.