In this monograph, group-theoretical approaches are used to build a system of hadrons and qualitatively describe the properties of chemical compounds. This serves as a complement to numerically and approximately solve the many-electron Schrödinger equation, in order to understand the behavior of chemical elements. Besides general theory, specific results are compared with experimentally measured chemical properties. Content: Symmetries of a quantum systemObservables of a quantum systemLie groups and Lie algebrasThe principles of particle classificationThe symmetry group of chemical elementsClassification and chemical properties of elementsAppendix A. Fock's energy spectrum of the hydrogen atomAppendix B. Representations of some groups