Resolution of Surface Singularities

We introduce the notions of modification and resolution. In the presence of a resolution of a surface singularity we also define the exceptional curve, the lattice generated by the irreducible exceptional curves together with its natural intersection form, its dual lattice and the Lipman cone. We prove several of their properties, e.g., the negative definiteness of the intersection from. The existence of a resolution and the uniqueness of the minimal one are also proved.