  We use an extension of Sunada's theorem to construct a nonisometric pair of
isospectral simply connected domains in the Euclidean plane, thus answering
negatively Kac's question, ``can one hear the shape of a drum?'' In order to
construct simply connected examples, we exploit the observation that an
orbifold whose underlying space is a simply connected manifold with boundary
need not be simply connected as an orbifold.
