An elevator the drive unit is arranged laterally in a top section of an elevator shaft and, as seen from a shaft door opening, at a side wall of the elevator shaft. At least one cable is guided over deflecting rollers of a support frame of the elevator car and over deflecting rollers of the counterweight and serves as a support and drive cable for the elevator car or the counterweight. The cable is guided over a drive pulley of the drive unit and is arranged transversely to the side wall. The support frame is constructed as a rucksack frame with an upright frame guided by guide rails and a horizontal base frame on which the elevator car is arranged. On travel to the uppermost stopping point, the upper part of the elevator car travels past the drive unit.