  This thesis discusses various aspects of duality in quantum field theory and
string theory. In the first part we consider duality in topological quantum
field theories, concentrating on the Donaldson and Seiberg-Witten theories as
(dual) approaches to the study of four-manifolds. Lower-dimensional variants of
these theories are also discussed. In the second part of the thesis we discuss
duality in 2D sigma models by studying the interplay between renormalization
group flows - as generated by the beta functions - and T-duality. The
hypothesis put forward in the thesis is that for these to be mutually
consistent, they should commute as operators in parameter space. The last part
of the thesis bring these subjects into perspective by reviewing some
nonperturbative dualities in string theory.
