Electron propagator theory provides a practical means of calculating electron binding energies, Dyson orbitals, and ground-state properties from first principles. This approach to ab initio electronic structure theory also facilitates the interpretation of its quantitative predictions in terms of concepts that closely resemble those of one-electron theories. An explanation of the physical meaning of the electron propagator's poles and residues is followed by a discussion of its couplings to more complicated propagators. These relationships are exploited in superoperator theory and lead to a compact form of the electron propagator that is derived by matrix partitioning. Expressions for reference-state properties, relationships to the extended Koopmans's theorem technique for evaluating electron binding energies, and connections between Dyson orbitals and transition probabilities follow from this discussion. The inverse form of the Dyson equation for the electron propagator leads to a strategy for obtaining electron binding energies and Dyson orbitals that generalizes the Hartree–Fock equations through the introduction of the self-energy operator. All relaxation and correlation effects reside in this operator, which has an energy-dependent, nonlocal form that is systematically improvable. Perturbative arguments produce several, convenient (e.g. partial third order, outer valence Green's function, and second-order, transition-operator) approximations for the evaluation of valence ionization energies, electron affinities, and core ionization energies. Renormalized approaches based on Hartree–Fock or approximate Brueckner orbitals are employed when correlation effects become qualitatively important. Reference-state total energies based on contour integrals in the complex plane and gradients of electron binding energies enable exploration of final-state potential energy surfaces. © 2012 John Wiley & Sons, Ltd.