  This dissertation reviews various aspects of the N=4 supersymmetric
Yang--Mills theory in particular in relation with the AdS/CFT correspondence.
The first two chapters are introductory. The first one contains a description
of the general properties of rigid supersymmetric theories in four dimensions
both at the classical and at the quantum level. The second chapter is a review
of the main properties of the N=4 SYM theory under consideration. Original
results are reported in chapters 3, 4 and 5. A systematic re-analysis of the
perturbative properties of the theory is presented in the third chapter. Two-,
three- and four-point Green functions of elementary fields are computed using
the component formulation and/or the superfield approach and subtleties related
to the gauge-fixing are pointed out. In the fourth chapter, after an
introduction to instanton calculus in supersymmetric gauge theories, the
computation of the one-instanton contributions to Green functions of gauge
invariant composite operators in the semiclassical approximation is reported.
The calculations of four-, eight- and sixteen-point Green functions of
operators in the supercurrent multiplet are reviewed in detail. The final
chapter is devoted to the AdS/SCFT correspondence. Some general aspects are
discussed. Then the attention is focused on the relation between instantons in
N=4 SYM and D-instanton effects in type IIB string theory. The comparison
between instanton contributions to Green functions of composite operators in
the boundary field theory and D-instanton generated terms in the amplitudes
computed in type IIB string theory is performed and agreement between these two
sources of non-perturbative effects is shown.
