Trondheim (, US: /ˈtrɒnheɪm/, Urban East Norwegian: [ˈtrɔ̂n(h)æɪm]; Southern Sami: Tråante; Kven: Tronjami; historically, Kaupangen, Nidaros and Trondhjem), is a city and municipality in Trøndelag county, Norway. It has a population of 205,332 as of 2020, and is the third most populous municipality in Norway, although the fourth largest urban area. Trondheim lies on the south shore of Trondheim Fjord at the mouth of the River Nidelva. The city is dominated by the Norwegian University of Science and Technology (NTNU), the Foundation for Scientific and Industrial Research (SINTEF), St. Olavs University Hospital and other technology-oriented institutions.

The settlement was founded in 997 as a trading post, and it served as the capital of Norway during the Viking Age until 1217. From 1152 to 1537, the city was the seat of the Catholic Archdiocese of Nidaros; since then, it has remained the seat of the Lutheran Diocese of Nidaros and the Nidaros Cathedral. It was incorporated in 1838. The current municipality dates from 1964, when Trondheim merged with Byneset, Leinstrand, Strinda and Tiller.

Trondheim has a very mild climate for its northerly latitude, resulting in moderate summers and winters that often remain above the freezing point in seaside areas. On higher elevation instead, the microclimate is colder and snowier.

The city functions as the seat of the County Mayor of Trøndelag county, but not as the administrative centre, which is Steinkjer. This is to make the county more efficient and not too centralized, as Trøndelag is the third largest county in Norway.

Trondheim is home to football club Rosenborg, Norway’s most successful team, as well as Granåsen Ski Centre which has hosted the World Championship in Cross-country skiing.