A corrector (1) for the axial and off-axial beam path of a particle-optical system, comprises a first (10) and a second (20) correction piece, which are disposed one behind the other in the beam path (2) on an optical axis (3). Each correction piece (10, 20) comprises four successive multipole elements (11, 12, 13, 14; 24, 23, 22, 21) disposed symmetrically with respect to a center plane (5) and with the following fields: wherein the first (11; 24) and the fourth (14; 21) multipole elements of the multipole elements (11, 12, 13, 14; 24, 23, 22, 21) are used to generate quadrupole fields (11′, 14′; 24′, 21′) and the second (12; 23) and third (13; 22) are used to generate octupole fields (12′″, 13′″; 23′″,22′″) and quadrupole fields (12′, 13′; 23′,22′), wherein the latter are superposed magnetic (12′, 13′; 23′, 22′) and electric fields (12″, 13″; 23″, 22″), wherein the quadrupole fields (11′, 12′, 13′, 14′; 24′, 23′, 22′, 21′) of all four multipole elements (11, 12, 13, 14; 24, 23, 22,21) are rotated from one to the next through 90°. An astigmatism of third order is corrected by a central multipole element disposed in the center plane and generating an octupole field.