The complexity of the Einstein Equations, which is due to their nonlinearity, makes a general analytical solution impossible. In order to extend the frontiers of our knowledge, physicists are especially interested in extreme scenarios. The strongest and thus most interesting source for the study of gravitational waves, a prediction of general relativity, is the merger of two black holes. To understand the generation and evolution of gravitational waves in such a case, extensive efforts have been made. One is the construction of highly sensitive detectors, which are likely to find gravitational wave signals. The other is extensive theoretical and computational efforts developing numerical treatments that simulate merging black holes. A substantial advance in research arose from the remarkable expansion of computing power in recent years. Yet, every attempt remains restricted by the specific requirements of a numerical setup. Based on the 3+1 formulation of Einstein’s equations presented by Arnowitt, Deser and Misner (ADM formalism), this thesis will provide a comprehensive discussion of suitable quantities, the Weyl scalars ψ [sub n], for the analysis of gravitational waves in numerical relativity, their features and their theoretical background. This presentation will be illustrated by a numerical simulation