The classical Hurwitz space is a fine moduli space for simple branched coverings of the Riemann sphere. The thesis investigates this space by using methods of complex differential geometry. We study a generalized Weil-Petersson metric on the Hurwitz space. For this purpose, Horikawa's deformation theory of holomorphic maps is developed in the presence of metrics. A curvature formula for a natural holomorphic subbundle of the tangent bundle on the Hurwitz space is given. From this, one can obtain the curvature of natural subspaces of this moduli space.
