  Duality symmetries in M--theory and string theory are reviewed, with
particular emphasis on the way in which string winding modes and brane wrapping
modes can lead to new spatial dimensions. Brane world-volumes wrapping around
Lorentzian tori can give rise to extra time dimensions and in this way
dualities can change the number of time dimensions as well as the number of
space dimensions. This suggests that brane wrapping modes and spacetime momenta
should be on an equal footing and M--theory should not be formulated in a
spacetime of definite dimension or signature.
