  This introductory part of the author's PhD compilation thesis discusses
non-perturbative aspects of string theory, with focus on D-instantons which
play key roles in the context of string phenomenology and dualities. By
translating ideas from ordinary instanton calculus in field theory, D-instanton
calculus is formulated and applied to supersymmetric gauge theories realized as
world volume theories of spacefilling D-branes in non-trivial backgrounds. We
show that, for configurations in which certain fermionic D-instanton zero modes
are either lifted or projected out, new couplings, which may be forbidden at
the perturbative level, are generated in the effective action, even though
their origin does not admit an obvious interpretation in terms of ordinary
field theory. Such couplings are of great relevance for semi-realistic MSSM/GUT
models since they can correspond to Yukawa couplings, Majorana mass terms for
right-handed neutrinos or Polonyi terms, relevant for supersymmetry breaking.
In the last part, we make use of various string dualities in order to compute
multi-instanton corrections which are otherwise technically difficult to obtain
from explicit D-instanton calculations. We compute one-loop diagrams with BPS
particles in type IIA string theory configurations, involving spacefilling
D-branes and orientifolds, and obtain exact quantum corrections in the dual
type IIB picture, including infinite series of D-instanton contributions. By
lifting the one-loop calculations to the M-theory picture, we obtain a
geometric understanding of the non-perturbative sector of a wide range of gauge
theories and elucidate the underlying symmetries of the effective action.
