Phase space structure of 4D symplectic mappings and applications to beam optics Ezio Todesco University of Bologna, INFN Sezione di Bologna, Italy e-mail: ETODESCO@bologna.infn.it The analytical tools of resonant normal forms for four dimensional symplectic mappings are outlined. The analysis of the perturbative series allows one to determine a classification of the resonant structures in phase space. In particular, the existence and the stability of fixed points for generic resonances and mappings is worked out. The analytical tools prove to be useful for the optimization of a magnetic lattice. An application to the sorting of the magnetic random errors of the LHC is outlined.