Science is built up from facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house (Henri Poincaré 1854-1912). If Mineralogy is to move beyond descriptive science, it needs a theoretical basis whereby we may understand and predict the structures, chemical compositions and behaviour of minerals in Earth processes at the scale of atoms and chemical bonds. The development of such a basis is the central theme of my work. The patterns of linkage of chemical bonds in space contain significant energetic information that may be used as the basis of a such an approach: Bond topology combines aspects of graph theory, topology, bond-valence theory, and the moments approach to the electronic-energy density-of-states to address many issues not addressed by established theoretical methods. I have deceloped a rigorous theoretical framework for the Structure Hierarchy Hypothesis, and derived such hierarchies for oxysalt (sulfate, borate, phosphate, vanadate, borate and beryllate) minerals. I have begun working on chain- and sheet-silicate minerals and a mathematically rigorous graph-theoretic approach to deriving all possible connectivities of tetrahedra and discovering what controls their occurrence in crystal structures. All papers are available as pdfs at frankhawthorne.com.