In this thesis, we present an expanded account of the work done by Neufang and Pirkovskii. Let X and Y be Banach spaces, ?? ? ??(??,??;?) is a nuclear operator if and only if there exist bounded sequences ???? ? ??? and ???? ? ??? such that T(x)(y)= ? ????(??) ? ??=? ????(??) ; ? ||????(??) ? ??=? || ||????(??)|| lt; ? For every x?X, y?Y. The nuclear norm of T is defined to be ||??|| = inf {? ||???? ? ??=? || ||????|| ? ??(??,??) = ? ????(??) ? ??=? ????(??),? ||????(??) ? ??=? || ||????(??)|| lt; ?}. Let G be a locally compact group equipped with a left Haar measure.