This monograph is a review of the quantum mechanical concepts presented in two other monographs, "The Nature of Atoms" and "Bonds Between Atoms," by the same author. It is assumed the reader is familiar with these ideas. The monograph sketches only those aspects of quantum mechanics that are of most direct use in picturing and calculating the behavior of atoms when they are stably bonded together in molecules and solids. Its emphasis is on stationary states; it does not deal with processes. The chapters are as follows: Wave-Like and Particle-Like Behavior; Probability and Stationary States; Uncertainty and the Particle in a Box; Schroedinger's Equation; Wave Functions, Operators, and The Harmonic Oscillator; Orthogonality and Kinetic Energy; The Variational Method of Approximation; The Spinning Electron; Symmetry and the Exclusion Principle. Problems are included at the end of each chapter. (PR)