Starting from the Swift sample we defined a complete sub-sample of 58
bright long Gamma Ray Bursts (GRB), 52 of them (90%) with a redshift determination, in
order to characterize their properties. This complete sample of bright long- GRBs allowed
us to investigate their evolution with cosmic time and properties. We focused in
particular on the GRB luminosity function, on the spectral-energy correlations of their
prompt emission, on the nature of dark bursts and on possible correlations between the
prompt and the X-ray afterglow properties.