  We present the general framework of \'Ecalle's moulds in the case of
linearization of a formal vector field without and within resonances. We
enlighten the power of moulds by their universality, and calculability. We
modify then \'Ecalle's technique to fit in the seek of a formal normal form of
a Hamiltonian vector field in cartesian coordinates. We prove that mould
calculus can also produce successive canonical transformations to bring a
Hamiltonian vector field into a normal form. We then prove a Kolmogorov theorem
on Hamiltonian vector fields near a diophantine torus in action-angle
coordinates using moulds techniques.
