The lasting stagnation of fundamental science becomes an increasingly urgent problem, especially by contrast to apparent success of its previous discoveries. In particular, the unsolved problems of quantum mechanics and particle theory strangely correlate with the stable absence of key advance in quantum computation and full-scale nanotechnology, despite the high promises and huge efforts applied. In this book the decisive extension of conventional science basis is introduced in the form of unreduced solution to the arbitrary interaction problem. It is shown how the qualitatively new, “dynamically multivalued” structure of the unreduced solution and real system behaviour leads to the intrinsically universal and problem-solving concept of dynamic complexity and chaos. It is applied here to problems of full-scale quantum computation and nanomachines, where the impossibility of unitary quantum machines is demonstrated together with the high potentialities of their extended, complex-dynamical version, already realised in natural living systems. The book is a mixture of rigorous basis, popular explanation and new paradigm discussion oriented to a wide range of educated readers.