  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.
