This thesis considers vortices in a superconductor and m a simple model and attempts to model two vortices close together. In contrast to superimposed vortices which have been described explicitly, we look to describe the separation of two vortices close together in terms of an expansion in the parameters, which describe their relative location. A simple model is used to describe two static vortices close together. An expansion m the parameters describing the relative position of the two vortices is derived in terms of trigonometric and exponential functions. The series solutions are derived from solving the relevant partial differential equations and are studied up to third order. A more realistic model, the Gmzburg-Landau theory of a superconductor in a magnetic field is studied. At the point between type-I and type-II superconductivity, this model has static vortex solutions, so-called Abrikosov vortices. Starting with two vortices on top of each other, we derive an expansion, which describes these two vortices close together. The expansion is studied up to third order. A similar pattern is found for the angular dependence in both models. The first simple model is shown to have some peculiar features only two vortices can be superimposed and when pulled apart a singularity at third order develops. In contrast, this does not happen in the Gmzburg-Landau model, which shows smooth solutions up to at least third order.