1. Introduction.- 2. Basis Set.- 2.A. Fundamental Concepts and General Description.- 2.B. Slater-Type Orbitals.- 2.C. Gaussian-Type Functions.- 2.D. Contracted Gaussian Basis Sets.- 2.E. Gaussian Expansion of Slater-Type Orbitals.- 2.F. Polarization Functions.- 2.G. Off-Centered Gaussian Functions.- 2.H. Comparison of Slater-Type and Contracted Gaussian Basis Sets.- 2.I. Remarks on the Selection of the Basis Set.- 3. SCF Calculations.- 3.A. Integrals over Slater-Type Orbitals.- 3.B. Integrals over Gaussian-Type Functions.- 3.C. Computer Time Saving in Evaluation of Integrals.- 3.D. Computer Time Saving in the SCF Procedure.- 4. Correlation Energy.- 4.A. Definition and Origin of the Correlation Energy.- 4.B. Conservation of the Correlation Energy.- 4.C. Empirical Calculations.- 4.D. Configuration Interaction.- 4.E. Independent Electron Pair Approximation.- 4.F. Cluster Expansion of the Wave Function.- 4.G. Many-Electron Theory of Sinanoglu.- 4.H. Coupled-Pair Many-Electron Theory.- 4.I. Coupled-Electron Pair Approximation.- 4.J. Perturbation Calculations.- 4.K. Numerical Treatment of Perturbation Expressions.- 4.L. Basis Set Dependence.- 4.M. Size Consistency.- 5. Applications.- 5.A. Molecular Geometries.- 5.B. Force Constants.- 5.C. Barriers to Internal Rotation and Inversion.- 5.D. Potential Curves.- 5.E. Thermochemistry.- 5.F. Chemical Reactivity.- 5.G. Ionization Potentials.- 5.H. Intermolecular Interactions.- 5.I. Solvation.- 5.J. Presence and Future.- Appendix A: Atomic Units.- Appendix B: Most Common Computer Programs.- References.