It has long been known that the non-linearity of the Hartree–Fock (HF) equations necessitates the existence of multiple self-consistent-field (SCF) solutions. This is especially true for systems containing unpaired electrons, or electrons with high angular momenta, or both, in which many low-lying HF solutions can be located. However, there has not been much concerted effort to analyse these solutions systematically to understand their behaviours and harness them in the treatment of electron correlation for ground and excited states. In this thesis, an analysis method based on symmetry via group and representation theories is first developed for the systematic classification of multiple HF solutions. The necessity of this method is then illustrated via an examination of the many low-lying HF solutions located for two model octahedral transition-metal complexes, [MF6]3– (M = Ti, V), that exhibit significant symmetry breaking, degeneracy or near-degeneracy, and strong electron correlation. This investigation, alongside previous results from others, reveals a common pattern of symmetry-broken HF solutions coalescing with other solutions and disappearing as the system descends away from high-molecular symmetry arrangements. This thus motivates a study on the possible relationships between various symmetry constraints and the reality of holomorphic HF wavefunctions that is carried out through an analytic model of [H4]2+. Finally, the symmetry and reality of HF solutions are re examined from a different perspective—that of elementary geometry based on a wavefunction distance metric defined via the space of density matrices—in the hope to obtain a better picture of the structure and topology of the SCF landscape.