  We review the issue of Borel summability in the framework of multiscale
analysis and renormalization group, by discussing a proof of Borel summability
of the $\phi^{4}_4$ massive euclidean planar theory; this result is not new,
since it was obtained by Rivasseau and 't Hooft. However, the techniques that
we use have already been proved effective in the analysis of various models of
consended matter and field theory; therefore, we take the $\phi^{4}_4$ planar
theory as a toy model for future applications.
