An electron-optical corrector for rendering superfluous both the third-order opening error and the anisotropic part of the extra-axial third-order coma, using round lenses and hexapole fields, the corrector includes at least three coaxially arranged hexapole fields with at least one round lens field is arranged between adjacent hexapole fields, so that the hexapole fields are imaged onto each other in pairs. The intensities of the hexapole fields are selected so that the image error coefficient of the three-fold astigmatism is equal to 0, and at least three hexapole fields in the Larmor reference system are rotated in relation to each other at an angle about the optical axis.