nice ideas have been so appealing that — the whole century after their conception — they are still very actively investigated. Both the higher dimensions of the Kaluza–Klein theory and Weyl’s higher-order curvature terms in an effective action are now incorporated into the foundations of string theory. Quadratic Gravity (QG) also plays an important role in contemporary studies of relativistic quantum field theories.

Quadratic Gravity is a very natural and quite “conservative” extension of the Einstein theory, the most precise gravity theory today. Quadratic terms in the QG Lagrangian can be understood as corrections to General Relativity, which may play a crucial role at extremely high energies. In the search for a consistent quantum gravity theory, which could be applicable near the Big Bang or near spacetime singularities inside black holes, it is important to understand the role of these higher-order curvature corrections.

Interestingly, it was suggested by Weinberg and Deser, and then proved by Stelle [@Stelle:77] already in the 1970s that adding the terms quadratic in the curvature to the Einstein–Hilbert action renders gravity renormalizable, see the very recent review [@Salvio]. This property is also preserved in the general coupling with a generic quantum field theory. However, due to 