  We provide a classification of entangled states that uses new discrete
entanglement invariants. The invariants are defined by algebraic properties of
linear maps associated with the states. We prove a theorem on a correspondence
between the invariants and sets of equivalent classes of entangled states. The
new method works for an arbitrary finite number of finite-dimensional state
subspaces. As an application of the method, we considered a large selection of
cases of three subspaces of various dimensions. We also obtain an entanglement
classification of four qubits, where we find 27 fundamental sets of classes.
