The present invention relates to a cylinder sleeve (10) having an outer mantle surface (11) that has a surface structure (12, 112, 212). According to the invention, it is provided that the mantle surface (11) is provided with elevations (13, 113, 213; 14, 118, 219), that each elevation (13, 113, 213; 14, 118, 219) has at least one rounded area (16, 116, 216) in the region of its base (B), that some of the elevations (13, 113, 213) have at least one undercut (15, 115, 215), and that at least one elevation (14, 118, 219) without undercut is disposed between two elevations (13, 113, 213) with undercut (15, 115, 215).