1.The Laws of Quantum Mechanics -- Introduction -- Observables and Variables -- The Conditions of Quantum Theory -- Angular Momentum -- The Principal Equations -- Dirac's Theory -- Spin and Magnetic Moment -- Phenomenological Description -- Semiclassical Theory of Radiation -- Fermi's Golden Rule -- Intensities of Transitions -- Second Quantization -- A Harmonic Oscillator -- The Fields of Bosons and Fermions -- Molecules -- Born -- Oppenheimer Approximation -- Chemical Bond -- Questions of Symmetry -- Point Groups -- Classification of States According to Symmetry -- 2.The Evolution of Perturbation Theory -- Preamble -- Frequencies and Intensities -- Perturbation Algebra -- Expansions of Two Types -- Many-Time Formalism -- Methods of Quantum-Field Theory -- Diagrams and Computational Rules -- Other Trends and Methods -- Alternative Perturbation Theory -- Canonical Transformation -- Hypervirial Result -- 3.Polynomials of Quantum Numbers -- The Principles of the Theory -- Recurrence Equations -- Many-Dimensional Case -- The Problem of Degenerate States -- Introduction to a Theory of Anharmonicity -- Advantages of the New Technique -- Polynomials and Computational Rules -- Electro-Optics of Molecules -- Phenomenon of Strong Anharmonicity -- The Direct and Inverse Problems of Spectroscopy -- Extraneous Quantum Numbers -- Factorization of the Matrix Elements -- The First Coefficients -- Calculation of Higher-Order Approximations -- Future Developments -- Functions of Quantum Numbers -- Background -- 4.Effects of Anharmonicity -- Extension to Magnetic Phenomena -- Magneto-Optical Anharmonicity -- An Electron in a Magnetic Field -- The Resonance Interaction -- Dimers in Low-Temperature Liquids -- Diatomic Dimers -- On the Theory of Overtones -- XH-XH Pairs -- 5.The Method of Factorization -- Algebraic Formalism -- Atom of Hydrogen Type -- Some Problems Involving Anharmonicity -- Poschl-Teller Potential -- Poschl-Teller-Like Potential -- Morse's Oscillator -- Generalized Morse's Oscillator.