NOVELTY - The rig (1) has a platform assembly (2) comprising a vertically oriented mast (5) and horizontally oriented booms (6). A radial segment supporting assembly (3) comprises a vertically oriented mast (8) and horizontally oriented booms (9) connected to the vertically oriented mast comprising a segment holding unit (10) at a distal end. A surface e.g. ground support boom (4), supports and levels the platform assembly and the radial segment supporting assembly. The booms of the platform assembly is moved and secured along a longitudinal axis of the boom and the mast.    USE - Assembly rig for assembling wind turbine towers or wind turbine tower sections on an installation side by using a ground support boom i.e. lorry trailer.    ADVANTAGE - The rig assembles the wind turbine towers or wind turbine tower sections on the installation side in a quick and easier manner. The rig provides an initial tower segment that can be positioned and held in an accurate position along three directions and with correct angles from where tower segments can be connected to initial tower segment correct positions and angles for the tower segments are achieved, so that the rig ensures a better working environment for workers. The lorry trailer is used as the surface, so that installation can be done in a faster and easier manner.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a method for assembling a wind turbine tower or a wind turbine tower section.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of an assembly rig.    Assembly rig (1)    Platform assembly (2)    Radial segment supporting assembly (3)    Ground support boom (4)    Vertically oriented mast of platform assembly (5)    Horizontally oriented booms of platform assembly (6)    Personnel basket (7)    Vertically oriented mast of radial segment supporting assembly (8)    Horizontally oriented booms of radial segment supporting assembly (9)    Segment holding units (10, 13)    Tower section (11)    Jacks (15)