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Non-relativistic quantum mechanics is a physical theory that, despite its exceptional empirical success, generated innumerable debates about its meaning since its first formulations in the early twentieth century. Both physicists and philosophers realized that the theory challenged many basic assumptions of traditional science and philosophy. Therefore, different interpretations were formulated to meet these challenges. This book introduces a new interpretation of quantum mechanics, the Modal-Hamiltonian Interpretation (MHI), which attempts to solve all the quantum puzzles from a unified perspective. It is hoped that this interpretation will be both reasonable for physicists in their daily practice and interesting for philosophers engaged in the metaphysics of science. This is a realist, non-collapse interpretation belonging to the family of Modal Interpretations and is expressed in algebraic formalism. The interpretation is modal because it adopts an irreducible concept of possibility and is Hamiltonian because the Hamiltonian operator of the quantum system defines the observables that acquire actual definite values. In this interpretative context, symmetries play a central role, both in the case of the symmetries of the Hamiltonian and regarding the role played by the Galilei group in interpretation. MHI can account for the measurement problem both in its traditional version and in the most recent measuring scenarios and, when applied to well-known physical models, it agrees with the everyday practice of physics. Its closed-system perspective leads to a top-down view of quantum mechanics according to which entanglement and decoherence are essentially relative phenomena.