Seiberg-Witten maps to all orders

All order Seiberg-Witten maps of gauge parameter, gauge field, and matter fields are given as a closed recursive formula. These maps are obtained by analyzing the order by order solutions of the gauge consistency and equivalence conditions as well as by directly solving Seiberg-Witten differential equations. The explicit third order non-Abelian and fourth order Abelian Seiberg-Witten maps of gauge parameter and gauge field are also presented.