The goal of this thesis has been to develop from scratch an ab initio computer program for calculating the electronic structure and properties of molecules. In order to obtain a good compromise between accuracy and computational cost, we decided to create a Hartree-Fock solver using Gaussian basis functions, as well as an implementation of Møller-Plesset perturbation theory up to third order. The thesis consists of three parts. Part I discusses the fundamentals of many-body quantum mechanics and derives the restricted andunrestricted Hartree-Fock equations. An optimised scheme for computing the one- and two-particle integrals needed for the calculation of the Fock matrix is described in detail. Finally, the Møller-Plesset perturbation theory up to third order is derived. Part II describes how we have implemented the methods in the C++ programming language, and the code is validated by reproducing a selection of published results. In part III we present and discuss results from calculations on various molecular systems. Both closed and open shell molecules are considered. Special attention is payed to the correlation energy and the problem of dissociation.