Complex sentence: Opened in 1877, the network has been operated since 1997 by Verkehrsbetriebe Karlsruhe GmbH, a company owned by the city of Karlsruhe, which was the network's operator between 1903 and 1997.
Split into simpler sentences: Opened in 1877, the network has been operated since 1997 by Verkehrsbetriebe Karlsruhe GmbH (VBK), a company owned by the city of Karlsruhe. The city itself was the tram network's operator between 1903 and 1997.