There are at least 4 dimensions in the universe - 3 space dimensions (length, breadth, depth), and one time dimension.
Beyond this, no one is really sure.
Some current theoretical physics models contain higher dimensions than this. See: http://en.wikipedia.org/wiki/String_theory
There are many different versions of String theory, however - some with more dimensions. One type known as M-theory ( http://en.wikipedia.org/wiki/M-theory ) has eleven space dimensions and one time, for a total of 12.
However, the universe is thought to be so narrow across these extra dimensions that for all practical purposes there are really only 4 we have to consider.
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