• Heat-Kernel
• Higher-Derivative gravity
• Quadratic gravity
• Scale symmetry
• Weyl geometry

In the thesis, a quadratic gravity model is extended to the case of a non-integrable Weyl geometry, where, in addition to Diffemorphism symmetry, a gauge boson is associated with local scale transformations. The study focuses on the renormalization flow properties of the theory. The 1-loop β-functions of the model were carried out by mean of the Heat-Kernel technique and their fixed points are defined. The result of the study indicates the presence of two different fixed point for the theory. For both fixed point the gravitational interaction presents asymptotic freedom, while the Weyl interaction presents two different trends, for a fixed point a trivial interaction is obtained, while in the second one we have asymptotic freedom. It should be noted, however, that, because of the technical complexity of the calculation, it was necessary to resort to an approximation in the computation of the β-function for the coupling of the Weyl boson. The final result is thus only qualitative and a future prospect is to complete the analysis of the model without any approximation.