Having mentioned the importance of cosmology and high energy astroparticle physics for experimental signatures of Quantum Gravity, another important guideline for the construction of a theory of Quantum Gravity is mathematical consistency. It turns out that it is highly non trivial to combine the principles of GR and QFT into one framework without running into contradictions. This has two aspects: First, mathematical techniques beyond those of QFT and GR need to be developed. Secondly, as there is no input from experiment so far there is no physical intuition about which aspects of the mathematical framework should be treated with care and which aspects can be handled in an intuitive way. All aspects must be analyzed rigorously. Accordingly, research in Quantum Gravity benefits greatly from interactions with several mathematical disciplines such as operator theory, functional analysis and measure theory. Quite in general methods from Mathematical Physics will play an important role in the development of Quantum Gravity.