In this thesis, I propose to interpret chemical rules and concepts from a topological, non-reductionist perspective. This is motivated by the fact that many chemical concepts such as aromaticity have been cornerstones of chemical thinking, despite precise quantum mechanical definitions remaining elusive. Instead of thinking about chemical rules in terms of well defined quantum mechanical entities, we promote the idea that a topological point of view in terms of adiabatic deformations is more appropriate and better attuned to the traditionally more intuitive and practical formulations of chemists. Based on the assumption that chemical concepts such as aromaticity provide accurate but abstract descriptors of nature, we explore their conceptual backgrounds from a physics perspective and connect them to ideas from the field of strong electronic correlations. In addition, our topological approach allows us to explore the interplay between chemical stability and the exotic topological properties of matter. While there are many chemical rules that predict the stability and structure of molecules and crystals, little is known about the connection between their topological properties and chemical stability, a topic especially important to strong correlation physics. Our approach provides us with a natural way to connect the more abstract topological concepts formulated in terms of model Hamiltonians with the structure-to-property relationships of chemical rules. We exemplify our approach by providing evidence for a new two-dimensional symmetry protected topological phase in decorated lattices and explore the topological properties of non-symmorphic materials found in monolayers of WTe2.