|We present here an introduction to Hartree-Fock theory in Quantum Chemistry.
From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. Additionally, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. Finally, the basic underlying concepts related to the construction and selection of Gaussian basis sets are discussed focusing in algorithmic efficiency issues. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.|