  We give a detailed account of the theory of position space renormalization
using graphical functions in the case of dimensionally regularized $\phi^4$
theory in four dimensions. In this theory we calculate the beta function, the
mass gamma function, and the self energy to seven loops in the minimal
subtraction scheme. The anomalous dimension $\gamma$ is calculated to loop
order eight.
  When possible, we generalize to even dimensions $\geq4$ with particular focus
on $\phi^3$ theory in six dimensions. In this theory we calculate the anomalous
dimension $\gamma$ to loop order six.
