Which of these German cities does not have a U-Bahn underground railway system?

Cologne does not have a U-Bahn underground railway system.

Rapid transit in Germany consists of four U-Bahn systems and fourteen S-Bahn systems. The U-Bahn or Untergrundbahn (underground railway) are conventional rapid transit systems that run mostly underground, while the S-Bahn or Stadtschnellbahn (city rapid railway) are commuter rail services, that may run underground in the city center as well but are classified as mainline railways.

There are four U-Bahn systems, namely in Berlin, Hamburg, Munich and Nuremberg; these are all run by the transit authorities in the city. Some cities call their Stadtbahn "U-Bahn" (like Frankfurt) or abbreviate their Stadtbahn with an U.

The term U-Bahn was created at the beginning of the 20th century in Berlin, where the 'Hochbahngesellschaft' (elevated railway company), operating elevated and suburban lines, decided they required an equally short and memorable name for their system as the S-Bahn, and chose to call it U-Bahn (with the U standing for 'Untergrund', German for underground). The name was soon adopted for Hamburg's city-owned independent mass transit tram lines.