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 system Observables of a quantum system Lie groups and Lie algebras The principles of particle classification The symmetry group of chemical elements Classification and chemical properties of elements Appendix A. Fock's energy spectrum of the hydrogen atom Appendix B. Representations of some groups