A corrector for chromatic and spherical aberration correction in an electron microscope with six multipoles (1, 2, 3, 4, 5, 6) arranged consecutively in the beam path symmetrically to a plane of symmetry, in such a manner that the first three (1, 2, 3) are before and the second three (4, 5, 6) after the plane of symmetry, all of which are used to produce quadrupole fields (1', 2', 3', 4', 5', 6') and octupole fields, wherein the quadrupole fields (1', 2', 3', 4', 5', 6') of all six multipoles (1, 2, 3, 4, 5, 6) are rotated through 90° from one to the next in relation to their field strengths and are point-symmetrical to the point of intersection of the optical axis with the plane of symmetry, wherein a replacement symmetry of the axial fundamental paths (x α, y β) with the plane of symmetry as the mirror plane for the replacement is created and wherein both the axial (x α, y β) and also the extra-axial fundamental paths (x γ, y δ) at the end of the corrector are guided together again, wherein through the interaction of the quadrupole fields (3', 4') configured as magnetic and electrical fields (3', 4') of the third and fourth multipole, a chromatic aberration correction is possible and also by setting octupole fields (3''', 4"') of the third and fourth multipole, which exert the same force effect direction on the electrons in the main sections (x, y) as the quadrupole fields (1', 2', 3', 4', 5', 6'), a correction of spherical aberrations and extra-radial aberrations which are produced by the corrector itself is possible, characterized in that the corrector can be arranged in the beam path in such a manner that the electron beam is radiated convergently to the optical axis in such a manner that the axial fundamental paths (x α, y β) only have maximum points (1.4, 15) in the regions of the third and fourth multipoles (3, 4), that a double multipole is arranged between the two centre multipoles (3, 4), which double multipole has a first multipole element before and a second multipole element after the plane of symmetry, wherein these multipole elements (11, 12) produce a first and a second octupole field (11', 12') which in the main sections (x, y) exert the same force effect direction on the electrons as the quadrupole fields (1', 2', 3', 4', 5', 6'), wherein the first multipole element additionally produces a third octupole field and the second multipole element additionally produces a fourth octupole field (12") which have different poles to one another and in respect of the first and second octupole field (11', 12') in the main sections (x, y) exert a force effect direction on the electrons that is rotated about 90 ° compared with the optical axis, that the third and four multipole (3, 4) produce mirror-symmetrical octupole fields (3''', 4''') at the intersection point of the optical axis and the plane of symmetry, the force effect direction of said octupole fields to the electrons in the main sections (x, y) corresponding to the first and second octupole field (11', 12') of the double multipole, but being rotated about 45 ° in respect of these, that the six multipoles (1, 2, 3, 4, 5, 6) produce octupole fields (1'', 2'', 3'', 4'', 5'', 6'') which exert a force effect direction on the electrons in the main sections (x, y) rotated about 90° in respect of the optical axis corresponding to the third and fourth octupole fields (11'', 12'') of the double multipole and in respect of field strength and algebraic sign are point-symmetrical to the point of intersection of the optical axis and the plane of symmetry, and that the setting of the poles and field strengths of the octupole fields (1'', 2'', 3'', 4'', 5'', 6'', 11'', 12'') rotated about 90 ° in respect of the force effect direction to the electrons in the aforementioned manner serves to correct the azimuth coma, with which the production of other aberrations is substantially avoided.