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Cologne (English: kə-LOHN; German: Köln [kœln]; Kölsch: Kölle [ˈkœlə]) is the largest city of Germany's most populous federal state of North Rhine-Westphalia and the fourth-most populous city in Germany With slightly over a million inhabitants (1.08 million) within its city boundaries, Cologne is the largest city on the Rhine and also the most populous city both of the Rhine-Ruhr Metropolitan Region, which is Germany's largest and one of Europe's major metropolitan areas, and of the RhinelandCentered on the left bank of the Rhine, Cologne is about 45 kilometres (28 mi) southeast of North Rhine-Westphalia's capital of Düsseldorf and 25 kilometres (16 mi) northwest of BonnIt is the largest city in the Central Franconian and Ripuarian dialect areas. The city's Cologne Cathedral (Kölner Dom) is the seat of the Catholic Archbishop of CologneThere are many institutions of higher education in the city, most notably the University of Cologne (Universität zu Köln), one of Europe's oldest and largest universities, the Technical University of Cologne (Technische Hochschule Köln), Germany's largest university of applied sciences, and the German Sport University Cologne (Deutsche Sporthochschule Köln), Germany's only sport university.

Cologne Bonn Airport (Flughafen Köln/Bonn) is Germany's seventh-largest airport and lies in the southeast of the cityThe main airport for the Rhine-Ruhr region is Düsseldorf Airport. Cologne was founded and established in Ubii territory in the 1st century AD as the Roman Colonia Claudia Ara Agrippinensium, the first word of which is the origin of its nameAn alternative Latin name of the settlement is Augusta Ubiorum, after the Ubii"Cologne", the French version of the city's name, has become standard in English as wellCologne functioned as the capital of the Roman province of Germania Inferior and as the headquarters of the Roman military in the region until occupied by the Franks in 462.

During the Middle Ages the city flourished as being located on one of the most important major trade routes between east and western EuropeCologne was one of the leading members of the Hanseatic League and one of the largest cities north of the Alps in medieval and Renaissance timesPrior to World War II, the city had undergone several occupations by the French and also by the British (1918–1926)Cologne was one of the most heavily bombed cities in Germany during World War II, with the Royal Air Force (RAF) dropping 34,711 long tons (35,268 tonnes) of bombs on the city. The bombing reduced the population by 95%, mainly due to evacuation, and destroyed almost the entire cityWith the intention of restoring as many historic buildings as possible, the successful postwar rebuilding has resulted in a very mixed and unique cityscape. Cologne is a major cultural centre for the Rhineland; it hosts more than 30 museums and hundreds of galleries.

Amsterdam (, UK also ; Dutch: [ɑmstərˈdɑm]) is the capital and most populous city of the Netherlands with a population of 872,680 within the city proper, 1,380,872 in the urban area and 2,410,960 in the metropolitan areaFound within the province of North Holland, Amsterdam is colloquially referred to as the "Venice of the North", attributed by the large number of canals which form a UNESCO World Heritage Site. Amsterdam's name derives from Amstelredamme, indicative of the city's origin around a dam in the river AmstelOriginating as a small fishing village in the late 12th century, Amsterdam became one of the most important ports in the world in the Dutch Golden Age of the 17th century and became the leading centre for finance and tradeIn the 19th and 20th centuries, the city expanded, and many new neighbourhoods and suburbs were planned and builtThe 17th-century canals of Amsterdam and the 19–20th century Defence Line of Amsterdam are on the UNESCO World Heritage List.

Sloten, annexed in 1921 by the municipality of Amsterdam, is the oldest part of the city, dating to the 9th century. As the commercial capital of the Netherlands and one of the top financial centres in Europe, Amsterdam is considered an alpha-world city by the Globalization and World Cities (GaWC) study groupThe city is also the cultural capital of the NetherlandsMany large Dutch institutions have their headquarters there, including Philips, AkzoNobel, TomTom and INGAlso, many of the world's largest companies are based in Amsterdam or have established their European headquarters in the city, such as leading technology companies Uber, Netflix and TeslaIn 2012, Amsterdam was ranked the second best city to live in by the Economist Intelligence Unit (EIU) and 12th globally on quality of living for environment and infrastructure by Mercer.

The city was ranked 4th place globally as top tech hub in the Savills Tech Cities 2019 report (2nd in Europe), and 3rd in innovation by Australian innovation agency 2thinknow in their Innovation Cities Index 2009The Port of Amsterdam is the fifth largest in EuropeAmsterdam Airport Schiphol is the busiest airport in the Netherlands, and the third busiest in EuropeFamous Amsterdam residents include the diarist Anne Frank, artists Rembrandt and Van Gogh, and philosopher Baruch Spinoza. The Amsterdam Stock Exchange is the oldest stock exchange in the worldAmsterdam's main attractions include its historic canals, the Rijksmuseum, the Van Gogh Museum, the Stedelijk Museum, Hermitage Amsterdam, the Concertgebouw, the Anne Frank House, the Scheepvaartmuseum, the Amsterdam Museum, the Heineken Experience, the Royal Palace of Amsterdam, Natura Artis Magistra, Hortus Botanicus Amsterdam, NEMO, the red-light district and many cannabis coffee shops.