  Given a knot K we introduce a new invariant coming from the Blanchfield
pairing and we show that it gives a lower bound on the unknotting number of K.
This lower bound subsumes the lower bounds given by the Levine-Tristram
signatures, by the Nakanishi index and it also subsumes the Lickorish
obstruction to the unknotting number being equal to one. Our approach in
particular allows us to show for 25 knots with up to 12 crossings that their
unknotting number is at least three, most of which are very difficult to treat
otherwise.
