  We provide a group-theoretical classification of the entangled states of N
identical particles. The connection between quantum entanglement and the
exchange symmetry of the states of N identical particles is made explicit using
the duality between the permutation group and the simple unitary group. Each
particle has n-levels and spans the n-dimensional Hilbert space. We shall call
the general state of the particle as a qunit. The direct product of the N qunit
space is given a decomposition in terms of states with definite permutation
symmetry. The nature of fundamental entanglement of a state can be related to
the classes of partitions of the integer N. The maximally entangled states are
generated from linear combinations of the less entangled states of the direct
product space. We also discuss the nature of maximal entanglement and its
measures.
