The Theory of Quanta has a large area of applicability. Any motion, at the fundamental level, is quantum-mechanical, or includes quantum-mechanical motion. Quantum Mechanics encompasses motion forms from atoms, to atomic nuclei, molecules, chemical binding, electric and magnetic fields, electromagnetic radiation, and transport phenomena. The book includes such quantum-mechanical theories, both in their standard form and original versions, with emphasis on their physical contents. 1) Ch. 1, The Atom, besides standard subjects, presents a new, original formulation of the Thomas-Fermi theory, which allows the possibility to arrive at new results like giant dipole oscillations in heavy atoms, atom ionization and chemical bonding. 2) Ch. 2, Molecules, puts emphasis on molecular spectra, including a semi-classical treatment of rotation spectra. The Jahn-Teller effect, with its various implications in many other areas, is discussed in detail. 3) Ch.3, The Atomic Nucleus, includes an original treatment of the nuclear dynamics, based on the mean-field idea. In particular, the Weizsacker mass formula is derived, nuclear instabilities are discussed and the statistical approach is presented. 4) Chs. 5-7 include an original presentation of the Electric and Magnetic Fields effects on atoms. The tunneling, both in static and oscillating electric fields, is presented, with application to atomic ionization, as well as the proton emission and the effect of high-intensity electric fields on alpha decay. The new subject of scattering of charges by laser pulses is presented in detail. 5) An interesting, new subject of transitions under change of parameters, including the dynamical Berry phase is given in Ch. 8, Change of Parameters. 6) Ch. 9, Stimulated Magnetic Resonance, presents a new phenomenon of magnetic resonance, generated by stimulated emission. 7) Ch. 10, Quantized Conductance, presents a new, original way of deriving the quanta of conductance in ballistic transport, or in magnetic field. 8) Ch. 11, Coherence, gives an extended account of the coherent interaction of the electromagnetic radiation with polarizable matter, with implication on the superradiance transition and possible new phenomena occurring in water. 9) Ch. 12, Chemical Bonding, is a description of the original theory of chemical bonding, based on the linearized Thomas-Fermi theory, with its basic application to formation of the metallic clusters. 10) Ch. 13, Quantum Theory of Radiation, is an exposition of the Dirac theory of radiation, and the interaction of the radiation with matter, following Fermi's famous article, a subject seldom presented in usual textbooks, in spite of its fundamental relevance. 11) The book ends with a thorough discussion of the place of the Quantum Mechanics in the realm of the Physical Science disciplines, emphasizing the fundamentally new, and very fruitful, quantum-mechanical vision.