This book provides a comprehensive account, from first principles, of the methods of numerical quantum mechanics, beginning with formulations and fundamental postulates. The development continues with that of the Hamiltonian and angular momentum operators, and with methods of approximating the solutions of the Schroedinger equation with variational and perturbation methods. Chapter 3 is a description of the Hartree-Fock self-consistent field method, which is developed systematically for atoms. The Born-Oppenheimer approximation is introduced, and the numerical methods presented one by one thereafter in a logically consistent way that should be accessible to undergraduates. These include LCAO, Hartree-Fock-SCF method for molecules, Roothaan LCAO-MO-SCF and electron correlation energy. Chapter 4 is devoted to the more sophisticated computational methods in quantum chemistry, with an introduction to topics that include: the zero differential overlap approximation; Huckel MO theory of conjugated molecules; Pariser-Parr-Pople MO method; extended Huckel theory; neglect of differential overlap methods; invariance in space requirements; CNDO; INDO; NDDO; MINDO; MNDO; AMNDO; AM1; MNDO-PM3; SINDO1; CNDI/S; INDO-CI; and ab initio. This is followed by an introduction to Moller-Plesset peturbation theory of many electrons, and coupled perturbed Hatree-Fock theory, with a description of the coupled cluster method. Finally, chapter 5 applies these methods to problems of contemporary interest. The book is designed to be a junior/senior level text in computational quantum mechanics, suitable for undergraduates and graduates in chemistry, physics, computer science and associated disciplines.