  We have constructed a complete hydrodynamic theory of nucleation and growth
in a one--dimensional version of an elastic shear martensitic transformation
with open boundary conditions where we have accounted for interfacial energies
with strain--gradient contributions. We have studied the critical martensitic
nuclei for this problem: Interestingly, the bulk critical nuclei are {\em
twinned} structures, although we have determined that the dominant route for
the formation of martensite is through {\em surface nucleation}. We have
analytically solved for the surface nuclei and evaluated exact nucleation rates
showing the strong preference for surface nucleation. We have also examined the
growth of martensite: There are two possible martensitic growth fronts, {\em
viz}., dynamical twinning and so-called two--kink solutions. These
transformation fronts are separated by a {\em dynamical} phase transition. We
analytically derive this phase diagram and determine expressions for the speeds
of the martensitic growth fronts.
