On hypergeometric systems of differential equations This thesis is about the hypergeometric system of differential equations. Until now fundamental solutions for this system are just known in dimension 2 and very special cases in higher dimension. In dimension 2 it is solvable with the hypergeometric function. Under some assumptions there exist characteristic constants for the system and in dimension 2 they can be represented by means of the Gamma function. In this work the solutions and constants of a hypergeometric system have been considered as power series in a newly introduced parameter. Furthermore two sequences of functions have been introduced and analyzed and the coefficients of the power series have been expressed in terms of these functions.