The invention relates to an implant (100) for partially replacing surfaces that are subject to stresses, especially the surfaces of a joint. Said implant comprises a spherical or axial, preferably cylindrical base (116) to be inserted in an area removed from the bone, e.g. a punched or drilled area. The base comprises at least one surface (104) for replacing the section (112) to be replaced and/or an adapter for receiving an element carrying the section, e.g. a joint surface element, tooth or pivot tooth. The system for inserting the implant comprises an angle determination system (10) in the form of elliptical plates (14, 16, 18) of different diameter and cutting angle to be placed onto the joint section to be restored to determine the angle and/or the size of the substitute material to be implanted, an angle guiding device (20) comprising a fixing extension (14, 16, 18, 30) to be inserted between the joint surfaces, and an angle adjusting device (24) linked with the fixing extension and comprising at least one guide element (26) whose angle can be adjusted or which can be disposed in an angle-defined position, for placing at least one guide wire (32) in the operation field or bore guide (40) for a tubular drill (60). The system further comprises a drill system that comprises at least one drill/punch (60) that can be guided through the bore guide (40). Said bore guide is held in a fixed relative position to the joint section to be restored either by the angle adjusting device (24) or by the guide wire (32). The invention further relates to an angle determining system in the form of elliptical plates (14, 16, 18), an oscillation drill device and hollow cylinder drills (64, 66) or punches having a beveled tip (68, 70).