This book presents a comprehensive account of a new member of the family of the modal interpretations of quantum mechanics. According to the modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the definition of systems and subsystems, and in the rule that selects the observables whose possible values become actual. This book begins by introducing the main interpretative postulates and by proving their Galilean invariance. Also discussed herein is an argument for the physical relevance of the interpretation.