  We present a general method to quantify both bipartite and multipartite
entanglement in a device-independent manner, meaning that we put a lower bound
on the amount of entanglement present in a system based on observed data only
but independently of any quantum description of the employed devices. Some of
the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell
inequality or the Svetlichny inequality, are shown to be tight. Besides,
device-independent entanglement quantification can serve as a basis for
numerous tasks. We show in particular that our method provides a rigorous way
to construct dimension witnesses, gives new insights into the question whether
bound entangled states can violate a Bell inequality, and can be used to
construct device independent entanglement witnesses involving an arbitrary
number of parties.
