  We present a general discussion of strings propagating on noncompact coset
spaces $G/H$ in terms of gauged WZW models, emphasizing the role played by
isometries in the existence of target space duality. Fixed points of the gauged
transformations induce metric singularities and, in the case of abelian
subgroups $H$, become horizons in a dual geometry. We also give a
classification of models with a single timelike coordinate together with an
explicit list for dimensions $D\leq 10$. We study in detail the class of models
described by the cosets $SL(2,\IR)\otimes SO(1,1)^{D-2}/SO(1,1)$. For $D\geq 2$
each coset represents two different spacetime geometries: (2D black
hole)$\otimes \IR^{D-2}$ and (3D black string)$\otimes \IR^{D-3}$ with
nonvanishing torsion. They are shown to be dual in such a way that the
singularity of the former geometry (which is not due to a fixed point) is
mapped to a regular surface (i.e.\ not even a horizon) in the latter . These
cosets also lead to the conformal field theory description of known and new
cosmological string models.
