The problem of rigorous description and understanding of intelligence and consciousness remains unsolved despite its quickly growing importance, including various applications, such as artificial intelligence and machine consciousness. This book presents a new approach to this problem based on the causally complete solution of the many-body problem with arbitrary interaction leading to the universal concept of dynamic complexity and chaoticity in terms of dynamic multivaluedness, or redundance, of explicitly emerging system realisations. Intelligence and consciousness are rigorously specified as certain, high enough levels of this unreduced complexity of natural or artificial brain dynamics, with their observed major properties (escaping otherwise scientifically exact explanation). It is shown then how the proposed concept of consciousness is closely related to the necessary global sustainability transition specified now as a step-like, unified growth of the level of consciousness and complexity in all human activities and approaches, in science and beyond. The book contains both the rigorous basis and popular discussion oriented to a wide audience of educated readers.