  In this paper we give a new, and shorter, proof of Huber's theorem which
affirms that for a connected open Riemann surface endowed with a complete
conformal Riemannian metric, if the negative part of its Gaussian curvature has
finite mass, then the Riemann surface is homeomorphic to the interior of a
compact surface with boundary, and thus it has finite topological type. We will
also show that such Riemann surface is parabolic.
