  We study systematically the Lax description of the KdV hierarchy in terms of
an operator which is the geometrical recursion operator. We formulate the Lax
equation for the $n$-th flow, construct the Hamiltonians which lead to
commuting flows. In this formulation, the recursion relation between the
conserved quantities follows naturally. We give a simple and compact definition
of all the Hamiltonian structures of the theory which are related through a
power law.
