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Regularity theory is one of the most challenging problems in modern theory of partial differential equations. It has attracted peoples eyes for a long history. A classical method of partial regularity theory is the freezing the coefficients method. The proof is complex and troublesome. And the result obtained by this method is not optimal. In this book, we use the method of A-harmonic approximation, to consider regularity theory for nonlinear partial differential systems. The new method not only allows one to simplify the procedure of proof, but also to establish optimal regularity results directly. This book should be useful to professionals in partial differential equations.