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We calculate corrections to the fermion propagator and to the Green'sfunctions of all fermion bilinear operators of the form $\bar\Psi \Gamma \Psi$,to one-loop in perturbation theory.  We employ the Wilson/clover action for fermions and a family of Symanzikimproved actions for gluons.  The novel aspect of our calculations is that they are carried out to secondorder in the lattice spacing, $O(a^2)$. Consequently, they have addressed anumber of new issues, most notably the appearance of loop integrands withstrong IR divergences (convergent only beyond 6 dimensions). Such integrandsare not present in $O(a^1)$ improvement calculations; there, IR divergent termsare seen to have the same structure as in the $O(a^0)$ case, by virtue ofparity under integration, and they can thus be handled by well-knowntechniques. We explain how to correctly extract the full $O(a^2)$ dependence;in fact, our method is generalizable to any order in $a$.  The $O(a^2)$ corrections to the quark propagator and Green's functionscomputed in this paper are useful to improve the nonperturbative RI-MOMdetermination of renormalization constants for quark bilinear operators.  Our results depend on a large number of parameters: coupling constant, numberof colors, lattice spacing, external momentum, clover parameter, Symanzikcoefficients, gauge parameter. To make these results most easily accessible tothe reader, we have included them in the distribution package of this paper, asan ASCII file named: Oa2results.m ; the file is best perused as Mathematicainput.

O(a^2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons