Abstract: Clifford analysis can be seen as a higher-dimensional equivalence to Complex Analysis, i.e. a higher-dimensional function theory. Unfortunately, due to the higher-dimensional nature, which implies non-commutativity of the underlying algebraic structure as well as non-isolating zeros of polynomials, classic methods from complex analysis do not work here and a different framework has to be developed. Here we will show how different mathematical tools, like Umbral calculus, group representations, Weyl-Heisenberg algebra, and others can be combined to create a function theory. In the end some applications will be given.