The fundamental Gauss-Bonnet theorem connects the geometry of the surface to its topology. It states that the mean curvature of the surface is related to the Euler characteristic. By using Hodge theory, this statement can be rephrased as a calculation of the index of a certain differential operator on the surface. This allows to look at the Gauss-Bonnet theorem as an instance of an index theorem. In this talk I will recall the statement of the Gauss-Bonnet theorem, I will explain the above interpretation of it and show some consequences of the mentioned point of view.