In this thesis, we describe the invariant ring of multipartite systems under the action of the stochastic local operations assisted with classical communication(SLOCC) group. To obtain the generators of the invariant ring we introduce the notions in classical invariant theory, geometric invariant theory, computational invariant theory and quantum information theory. From these descriptions, we compute the subalgebra analog to Grobner bases for ideals(SAGBI) bases. Finally, we introduce other approach to obtain the invariants of k-qubit states by using the invariants of (k-1)-qubits states, and prove the statement that a separable state is an unstable point by using the Hilbert-Mumford criterion.