  In this paper I present a new class of traversable wormholes. This is done by
surgically grafting two Schwarzschild spacetimes together in such a way that no
event horizon is permitted to form. This surgery concentrates a non--zero
stress--energy on the boundary layer between the two asymptotically flat
regions. I shall investigate this stress--energy in detail using the "junction
condition" formalism. A feature of the present analysis is that this class of
traversable wormholes is sufficiently simple for a (partial) dynamical
stability analysis to be carried out. The stability analysis places constraints
on the equation of state of the exotic matter that comprises the throat of the
wormhole.
