An illumination system (12) of a microlithographic exposure apparatus (10) comprises a condenser (601; 602; 603; 604; 605; 606) for transforming a pupil plane (54) into a field plane (62). The condenser has a lens group (L14, L15, L16, L17; L24, L25, L26, L27, L28; L34, L35, L36, L37; L44, L45, L46; L53, L54, L55) that contains a plurality of consecutive lenses. These lenses are arranged such that a light bundle (70) focused by the condenser (601; 602; 603; 604; 605) on an on-axis field point (72) converges within each lens of the lens group. At least one lens (L15, L16, L17; L25, L26; L34, L44, L45; L54) of the lens group has a concave surface. The illumination system may further comprise a field stop objective (66; 666, 666′) that at least partly corrects a residual pupil aberration of the condenser (601; 602; 603; 604; 605; 606).