It is well known that when a magnetic field is applied to so-called type II superconductors, magnetic flux is able to penetrate in quantized amounts by forming cylindrical domains known as vortices. Within a vortex core, the superconductivity is suppressed, and single-particle excitations are observed. In this thesis, we calculate the local density of states for an isolated vortex using a variety of order parameters. The calculations are performed within the framework of the quasiclassical Eilenberger theory. We find that the states within the core do not represent those of the normal region. Instead, the distribution of the local density of states is characterized by the order parameter.