The Dawn of the Quantum Theory -- A. Complex Numbers -- The Classical Wave Equation -- B. Probability and Statistics -- The Schrodinger Equation and a Particle in a Box -- C. Vectors -- The Postulates and General Principles of Quantum Mechanics -- D. Series and Limits -- The Harmonic Oscillator and Vibrational Spectroscopy -- E. Spherical Coordinates -- The Rigid Rotator and Rotational Spectroscopy -- F. Determinants -- The Hydrogen Atom -- G. Matrices -- Approximation Methods -- H. Matrix Eigenvalue Problems -- Many-Electron Atoms -- The Chemical Bond: One- and Two-Electron Molecules -- Qualitative Theory of Chemical Bonding -- The Hartree--Fock--Roothaan Method.