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