Perturbative quantum field theory (pQFT) entails the process of renormalization: the iterated subtraction of subdivergences of Feynman diagrams, culminating in the subtraction of an overall divergence (or addition of a counterterm) that renders each diagram finite and delivers its contribution to the appropriate renormalized Green function. Many people helped to develop this process, though it has become customary to record the work of Bogoliubov and Parasuik (1957), Hepp (1966), and Zimmermann (1969) (BPHZ), completed by the forest formula in Zimmermann (1969), almost 30 years ago. A review is provided by the textbook of Collins (1986). In addition to the BPHZ formalism one needs analysis, to evaluate regularized expressions for the bare diagrams, prior to renormalization. Much progress has been made in this direction by combining dimensional regularization (t'Hooft and Veltman, 1972) and integration by parts, for massless (Chetyrkin and Tkachov, 1981) and massive (Broadhurst, 1992; Avdeev, 1996; Broadhurst, 1998) diagrams with up to three loops, together with more ad hoc techniques at higher loops. Since 1981 it was possible, in principle, to obtain the four-loop /3-function
