Staggered fermions and their O(a) improvements

Expanding upon the arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order a terms in the staggered fermion action. We propose a general program to improve fermion operators to remove O(alpha) corrections from their matrix elements, and demonstrate this program for the examples of matrix elements of fermion bilinears and B-K. We also determine the additional operators which must be added to improve the standard staggered fermion currents.