In this chapter, I introduce all necessary background concepts which lay the technical foundations for this thesis, focusing on the AdS/CFT correspondence as well as selected topics from condensed matter and quantum information theory. The guiding principle for all investigations in this thesis is to make progress towards a theory of quantum gravity. Such a theory, though elusive, is expected to have several features which can be investigated in a more controlled way when working within the framework of the AdS/CFT correspondence.