The representation dimension of an artin algebra as introduced by M.Auslander
in his Queen Mary Notes is the minimal possible global dimension of the
endomorphism ring of a generator-cogenerator. The paper is based on two texts
written in 2008 in connection with a workshop at Bielefeld. The first part
presents a full proof that any torsionless-finite artin algebra has
representation dimension at most 3, and provides a long list of classes of
algebras which are torsionless-finite. In the second part we show that the
representation dimension is adjusted very well to forming tensor products of
algebras. In this way one obtains a wealth of examples of artin algebras with
large representation dimension. In particular, we show: The tensor product of n
representation-infinite path algebras of bipartite quivers has representation
dimension precisely n+2
