This book presents a complete review of the theory of nonlinear quantum mechanics and which differs totally from the original discipline of quantum mechanics as well as the studies the nature of microscopic particles under action of the nonlinear interactions in the systems; which give numerous new and interesting properties and rules of motions of the particles, such as wave-corpuscle duality and localization, and which discusses the applications of theory as relates to condensed matter, polymers, and biological systems. It is intended for researchers, teachers, graduate students and upper-level undergraduate students. The so-called discipline of nonlinear quantum mechanics (NLQM) is, in reality, only a theory for studying the properties and motion of microscopic particles (MIPs) in nonlinear physical systems. It was so named in relation to the concept of quantum mechanics established by Bohr, Heisenberg, Schrödinger and numerous others. The latter deals only with the properties and motion of microscopic particles in linear systems without nonlinear interactionh and will, here-in-after, referred to as linear quantum mechanics (LQM). The following topics are covered in 6 chapters i