Spectra and essential spectra of selfadjoint and essentially selfadjoint operators -- Schrรถdinger operators -- Perturbations small at infinity -- Examples -- Operators acting only on part of the variables -- N-particle Hamiltonians -- Symmetries of the Hamiltonian -- The spectrum of the Hamiltonian of a free system -- A lower bound of the essential spectrum -- The essential spectrum of the Hamiltonian of an N-particle system with external forces -- The essential spectrum of the internal Hamiltonian of a free system -- Proof of theorem 11.16