  In this paper, we introduce the integration of algebroidal functions on
Riemann surfaces for the first time. Some properties of integration are
obtained. By giving the definition of residues and integral function element,
we obtain the condition that the integral is independent of path. At last, we
prove that the integral of an irreducible algebroidal function is also an
irreducible algebroidal function if all the residues at critical points are
zeros.
