Abstract: An apparatus for the variable machining of workpieces is described which consists of a central module, which is constructed as a hollow carrier unit and which takes over the functions of the machine housing, and also of a plurality of horizontal and vertical modules which can be selectively connected with this central module and with one another via predetermined mechanical and electrical interfaces. The central module has an outwardly disposed and rotatably mounted carrier sleeve which can be axially displaced by a restricted amount, which can also be clamped, and which has mounts for tool support units, with the mounts extending over only part of the height of the carrier sleeve and being distributed around its periphery. The inner chamber of the central module is provided with fitted guide surfaces for a vertical module which is constructed as a columnar unit with a base end connection surface and with external guide surfaces complementary to the guide surfaces of the central module.