In 1928, Paul Dirac derived the Dirac equation that provided the first relativistic description of an electron. Dirac-Hartree-Fock (DHF) theory is a relativistic generalization of Hartree-Fock theory that works by using the Hamiltonian from the Dirac equation instead of the Schrödinger equation. In this worksheet, we give a theoretical background on DHF theory culminating in a derivation of the Dirac-Hartree-Fock-Roothaan equations for the large and small components of the Dirac spinors. Then we compare nonrelativistic values from HF theory for the total electronic energy of an isoelectronic series of molecules CH4, SiH4, and GeH4, to the values found with DHF method, to see how relativistic effects rapidly become more significant for heavier atoms. This worksheet uses the Maple Quantum Chemistry Toolbox.