Lie groups are an indispensable tool in quantum mechanics, quantum chromodynamics, and gauge theories. The algebraic structure of these mathematical groups forms the basis in physics for describing the properties of symmetries. The only German-language textbook on the subject provides, in addition to fundamental chapters on groups and algebraic representation, a detailed introduction to Lie groups and Lie algebras. Subsequently, readers can deepen their understanding of the material through the calculation of advanced Lie algebras. The textbook offers a systematic and compact introduction to the mathematical foundations of Lie theory with the aim of understanding symmetries as one of the most essential topics in modern physics. Beginning with a discussion of groups and their linear representations, Lie groups and Lie algebras are addressed both in abstract form and in concrete applications.