  The recent developments of the ``connection'' and ``loop'' representations
have given the possibility to show that the two representation are equivalent
and that it is possible to transform any result from one representation into
the other. The glue between the two representations is the loop transform. Its
use, combined with the techincs Penrose's binor calculus, gives the possibility
to establish the exact correspondence between operators and states in the
connection representation and those in the loop representation.
  The main ingredients in the prove of the equivalence are: the concept of
embedded spin network, the Penrose graphical method of SU(2) calculus, and the
existence of a generalized measure on the space of connections.
