  We give an introduction to the theory of multi-partite entanglement. We begin
by describing the "coordinate system" of the field: Are we dealing with pure or
mixed states, with single or multiple copies, what notion of "locality" is
being used, do we aim to classify states according to their "type of
entanglement" or to quantify it? Building on the general theory of
multi-partite entanglement - to the extent that it has been achieved - we turn
to explaining important classes of multi-partite entangled states, including
matrix product states, stabilizer and graph states, bosonic and fermionic
Gaussian states, addressing applications in condensed matter theory. We end
with a brief discussion of various applications that rely on multi-partite
entangled states: quantum networks, measurement-based quantum computing,
non-locality, and quantum metrology.
