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PINOCCHIO generates catalogues of cosmological dark matter halos with known mass, position, velocity and merger history. It is able to reproduce, with very good accuracy, the hierarchical formation of dark matter halos from a realization of an initial (linear) density perturbation field, given on a 3D grid. Its setup is similar to that of a conventional N-body simulation, but it is based on the powerful Lagrangian Perturbation Theory. It runs in just a small fraction of the computing time taken by an equivalent N-body simulation, producing promptly the merging histories of all halos in the catalog.