  We give a extensive account of a recent new way of applying the Dirichlet
form theory to random Poisson measures. The main application is to obtain
existence of density for thelaws of random functionals of L\'evy processes or
solutions of stochastic differential equations with jumps. As in the Wiener
case the Dirichlet form approach weakens significantly theregularity
assumptions. The main novelty is an explicit formula for the gradient or for
the "carr\'e du champ' on the Poisson space called the lent particle formula
because based on adding a new particle to the system, computing the derivative
of the functional with respect to this new argument and taking back this
particle before applying the Poisson measure. The article is expository in its
first part and based on Bouleau-Denis [12] with several new examples,
applications to multiple Poisson integrals are gathered in the last part which
concerns the relation with the Fock space and some aspects of the second
quantization.
