  There are three new things in this paper about the open symmetrized bidisk
$\mathbb G = \{(z_1+z_2, z_1z_2) : |z_1|, |z_2| < 1\}$. They are motivated in
the Introduction. In this Abstract, we mention them in the order in which they
will be proved.
  \begin{enumerate} \item The Realization Theorem: A realization formula is
demonstrated for every $f$ in the norm unit ball of $H^\infty(\mathbb G)$.
\item The Interpolation Theorem: Nevanlinna-Pick interpolation theorem is
proved for data from the symmetrized bidisk and a specific formula is obtained
for the interpolating function. \item The Extension Theorem: A characterization
is obtained of those subsets $V$ of the open symmetrized bidisk $\mathbb G$
that have the property that every function $f$ holomorphic in a neighbourhood
of $V$ and bounded on $V$ has an $H^\infty$-norm preserving extension to the
whole of $\mathbb G$. \end{enumerate}
