Many differential equations describing time evolution equations are expressions of invariants associated to some Lie group and the theory of these groups provides a unifying viewpoint for the study of all special functions and all their properties. In fact, Sophus Lie invented the theory of Lie groups when studying the symmetries of differential equations. The integration of a (partial) differential equation by the method of separation of variables or by Lie algebraic methods is intimately connected with the existence of symmetries. For example, the exact solubility of the Schrödinger equation in quantum mechanics can be traced back to the underlying invariances. In the latter case, the investigation of symmetries allows for an interpretation of the degeneracies, where different configurations to have the same energy, which generally occur in the energy spectrum of quantum systems. Continuous symmetries in physics are often formulated in terms of infinitesimal rather than finite transformations, i.e. one considers the Lie algebra rather than the Lie group of transformations