  Two dimensional classical string theory is solved in any curved spacetime.
The complete spacetime required to describe the classical string motions turns
out to be larger than the global space required by complete particle geodesics.
The solutions are fully classified by their behavior in the asymptotically flat
region of spacetime. When the curvature is smooth, the string solutions are
deformed folded string solutions as compared to flat spacetime folded strings
that were known for 19 years. However, surprizing new stringy behavior becomes
evident at curvature singularities such as black holes. The global properties
of the classical string theory require that the ``bare singularity region'' of
the black hole be included along with the usual black hole spacetime. The
mathematical structure needed to describe the solutions include a recursion
relation that is analogous to the transfer matrix of lattice theories. This
encodes lattice-like properties on the worldsheet on the one hand and the
geometry of spacetime on the other hand. A case is made for the presence of
folded strings in the quantum theory of non-critical strings for $d\geq 2$.
