  {}~~~We show that the recently constructed $~N=4$~ supersymmetric self-dual
Yang-Mills theory as the consistent background of \hbox{$~N=2$} open
superstring will generate Witten's topological field theory in two-dimensions
as a descendant theory after appropriate twisted dimensional
reduction/truncations. We also show that this topological field theory further
generates supersymmetric Korteweg de Vries equations, $~SL(n)\-$Toda theory and
$~W_\infty\-$gravity in the $~n\rightarrow\infty$~ limit. Considering also that
this topological field theory is to generate other integrable and topological
systems, our results give supporting evidence for the conjecture that the
$~N=2$~ open superstring theory is the underlying ``master theory'' of
integrable and topological systems, {\it via} the intermediate $~N=4$~
supersymmetric self-dual Yang-Mills theory as its consistent target space-time
background.
