A transmission system including a shift mechanism for operating and controlling the transmission system. To automatically detect geometric characteristic values of the transmission system or of the shifting device a selector motor and a shift motor actuate a select or finger that is displaceably mounted in a selection-shift-passageway layout. Starting from an initial position whose coordinates within the selection-shift-passageway layout are unknown, the selector finger is displaced in the directions of shifting and in the directions of selection in order to detect paths of movement in the direction of selection or shifting. The selector finger is repeatedly displaced to establish the maximum paths of movement until the predetermined transmission geometric characteristic values are completely detected. Also disclosed are a control device for controlling a transmission system that includes a shift mechanism, and a method for controlling such a transmission system.