The invariance property of the Riemann function and a method of its construction

B. Riemann suggested "the Riemann principle of integrating" as applied to a hyperbolic second-order partial equation in two independent variables. In order to apply the method it is necessary to construct Riemann function that is a solution of Cauchy special characteristic problem. General method for Riemann function construction doesn't exist. We show the Riemann function is invariant with respect to the fundamental solutions symmetries and suggest a method for its construction.