"Both classical and quantum corrections can be analyzed by a perturbative approach based on the so-called weak field approximation. The heart of Einstein’s theory is represented by its ten coupled partial differential equations. The solutions of these equations, i.e., the gravitational potentials, are the metric tensor components. In the weak field approximation, the metric tensor can be decomposed in two terms: the flat Minkowski metric and the small perturbation multiplied by the gravitational constant. The solution of the non-linear equations can be considered the sum of infinite terms, and Newton’s theory emerges in the linear order. ... used this approximation to investigate the infinities that emerge by applying the early QFT techniques to quantize the gravitational interaction (Rosenfeld, 1930). Different kinds of divergent quantities had already appeared in the context of QED at the end of the 1920s: their correct treatment will be clarified only after the Second World War."