This thesis is dedicated towards the development of a novel boundary element method for scattering problems governed by the wave equation. Although these problems are posed on the unbounded exterior of the scatterer, the boundary integral equation method facilitates a reduction to the bounded surface of the scatterer. The strong Huygens principle bestows a special structure upon the integral operators of the wave equation in three spatial dimensions, reverberating through their name "retarded potentials". Space-time discretization methods treat both the continuous as well as the discretized problem as a single operator equation in the 3+1-dimensional space-time cylinder. The proposed scheme is based on unstructured simplex meshes of the lateral boundary of this cylinder. Well-established space-time variational formulations are discretized by means of piecewise polynomial trial spaces defined on these meshes. Integral representations of retarded potentials are derived, which genuinely conform to the space-time setting. Furthermore, this work provides quadrature techniques for pointwise evaluations of retarded potentials as well as the evaluation of energetic bilinear forms. Numerical experiments are exhibited, verifying the implementation and the capacity of the proposed space-time approximation method.weiterlesen