This course introduces quantum field theory and in particular renormalization theory and Dyson--Schwinger equations from the viewpoint of Hochschild cohomology.

Syllabus An optimistic overview of what could be covered.

Three reviews are:

Review (D.Kreimer, Fields Inst.Comm.50 (2007) 225).

Review (C.Bergbauer, D.Kreimer, IRMA Lect.\ Math.\ Theor.\ Phys.\ {\bf 10} (2006) 133.

Review (D.Manchon, preprint)

For gauge theories, see

Dirk's Anatomy (D.Kreimer)

Walter van Suijlekom's paper

paper on non-perturbative QED