  A review of the applications of noncommutative geometry to a systematic
formulation of duality symmetries in string theory is presented. The spectral
triples associated with a lattice vertex operator algebra and the corresponding
Dirac-Ramond operators are constructed and shown to naturally incorporate
target space and discrete worldsheet dualities as isometries of the
noncommutative space. The target space duality and diffeomorphism symmetries
are shown to act as gauge transformations of the geometry. The connections with
the noncommutative torus and Matrix Theory compactifications are also
discussed.
