The approach of calculating non-perturbative effects in Quantum Chromodynamics by expanding about non-trivial classical solutions of the equation of motion is described. Some of the techniques required for this are developed in references [l,2,3] on which this thesis is predominantly based. The general self-dual solutions are discussed. With these as background fields the Green and massless Dirac functions are solved for arbitrary group representation. Then with the help of these the determinants and collective coordinate zero modes required for the first order quantum corrections ar'3 calculated.