Abstract
Perturbative renormalization theory may not be a topic of CQFT, but it does have a long and rich history and is the basis of every textbook account of QFT. Still, few students really understand it. This is hardly surprising since no text really explains it. I believe that it is possible to give a simple and complete account of perturbative renormalization, and it is fitting that I try to do so in a school on CQFT; for the approach I shall advocate shares a number of ideas with current work in CQFT, and an understanding of the cancellation of ∞’s in perturbation theory is important for an understanding of what happens in the “small field region” of CQFT.
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