  In this paper, we mainly discuss the separability of $n$-partite quantum
states from elements of density matrices. Practical separability criteria for
different classes of $n$-qubit and $n$-qudit quantum states are obtained. Some
of them are also sufficient conditions for genuine entanglement of $n$-partite
quantum states. Moreover, one of the resulting criteria is also necessary and
sufficient for a class of $n$-partite states.
