We consider a function theory for functions defined in Rn with values in the quaternions or in Clifford algebras. The class of monogenic functions is firstly defined as the set of null solutions of a generalized CauchyRiemann system. Basic elements of this function theory (see also [1],[2]) like integral formulas, derivability, series expansions and geometric mapping properties will be briefly discussed. As an example for possible applications we deal with a generalized hypercomplex Beltrami equation (see [3]). References [1] K. Gürlebeck, K. Habetha, W. Sprößig, Holomorphic Functions in the Plane and ndimensional Space, Basel: Birkhäuser. xiii, 394 p. (2008). [2] K. Gürlebeck, K. Habetha, W. Sprößig, Application of Holomorphic Functions in Two and higher dimensions, Birkhäuser Verlag, Basel, 2016, xv, 390 p. [3] K. Gürlebeck and U. Yüksel (2018), On a Dirichlet Problem for a Generalized Beltrami Equation, Adv. Appl. Clifford Algebras, in press.
