Dimensions[expr] gives a list of the dimensions of expr.
Dimensions[expr, n] gives a list of the dimensions of expr down to level n.
expr must be a full array, with all the pieces of expr at a particular level having the same length. (The elements of expr can then be thought of as filling up a hyper-rectangular region.)
Each successive level in expr sampled by Dimensions must have the same head.
Example: Dimensions[a,b,c,d,e,f] .
See The Mathematica Book: Section 1.8.3 and Section 3.7.3.
See also: TensorRank, VectorQ, MatrixQ.