  We review the theory of multi-particle entanglement. In this book chapter we
aim at briefly ``setting the coordinates'' and guiding through the extensive
literature in this field. Our coordinate system chosen for this chapter has the
axes labeled pure and mixed states on the one hand, entanglement in single
specimens and the asymptotic setting on the other hand. We very briefly mention
ways to detect multi-particle entanglement, and introduce the concepts of
stabilizer and graph states.
