A riveting apparatus for creating a plurality of rivet joints along the surface of a workpiece includes a tool device controllable by tool control data in order to create countersunk holes on the workpiece and to set countersunk rivets in the created countersunk holes. The riveting apparatus also includes a programmable control device to generate the tool control data for the tool device and an optical sensing device for optically sensing the workpiece surface and for supplying sensing data. The control device evaluates the sensing data in order to obtain geometric data that represent at least one geometric parameter of a countersunk hole that has already been created, and to correct as required the tool control data for a countersunk hole that is subsequently to be created based on the result of an evaluation of the obtained geometric data.