Computing the \theta-exact Seiberg-Witten map for arbitrary gauge groups

We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in the gauge coupling constant or, equivalently, in the number of ordinary gauge fields. We do so for arbitrary compact gauge groups in arbitrary unitary representations. For gauge and matter fields, we fully work out \theta-exact non-hybrid Seiberg-Witten maps up to order three in the number of ordinary gauge fields.