Measuring entanglement

The physics literature in the last 10 years contains an immense number of papers related to multi-particle entanglement involving some very sophisticated mathematics. In this lecture we will survey some of this work that centers on geometric invariant theory. Most of the concrete work has been done for at most 4 qubits. There are several reasons for this. One is the combinatorial explosion which we will explain and another is that for 2,3 or 4 qubits SLOCC is related to deep properties of SO(4), SO(8) and F_4.