  We present an unifying approach to the quantification of entanglement based
on entanglement witnesses, which includes several already established
entanglement measures such as the negativity, the concurrence and the
robustness of entanglement. We then introduce an infinite family of new
entanglement quantifiers, having as its limits the best separable approximation
measure and the generalized robustness. Gaussian states, states with symmetry,
states constrained to super-selection rules and states composed of
indistinguishable particles are studied under the view of the witnessed
entanglement. We derive new bounds to the fidelity of teleportation d_{min},
for the distillable entanglement E_{D} and for the entanglement of formation. A
particular measure, the PPT-generalized robustness, stands out due to its easy
calculability and provides sharper bounds to d_{min} and E_{D} than the
negativity in most of states. We illustrate our approach studying
thermodynamical properties of entanglement in the Heisenberg XXX and dimerized
models.
