Köln (also known as Cologne in English) is a city located in western Germany. Here are a few options for getting to Köln from Madrid:
By plane: The fastest way to get to Köln from Madrid is by taking a flight from Madrid Barajas Airport to Köln/Bonn Airport. Several airlines offer flights between the two cities, and the flight time is around 2 hours.
By train: The fastest way to travel by train from Madrid to Köln is to take the AVE high-speed train to Paris and then transfer to a Thalys train to Köln. The entire trip takes around 13 hours.
By bus: Several bus companies operate routes between Madrid and Köln, and the trip takes around 40 hours. Buses depart from the Estación de Autobuses de Avenida de América in Madrid.
By car: You can also drive to Köln from Madrid, although the trip is quite long and takes around 22 hours via the A-2, A-61, and A-3 highways.
It's worth noting that Köln is located in Germany, so if you're coming from Madrid, you'll be crossing international borders. You'll need to bring your passport and be prepared to go through customs.