The Faroe or Faeroe Islands are an archipelago in the North Atlantic Ocean and an autonomous territory of the Kingdom of Denmark. The official language of the country is Faroese, which is closely related to and partially mutually intelligible with Icelandic.

Located 320 kilometres (200 mi) north-northwest of the United Kingdom, the islands have a total area of about 1,400 square kilometres (540 sq mi) with a population of 54,676 as of August 2023. The terrain is rugged, and the subpolar oceanic climate (Cfc) is windy, wet, cloudy, and cool. Despite the northerly climate, the temperatures are moderated by the Gulf Stream and average above freezing throughout the year, hovering around 12 °C (54 °F) in summer and 5 °C (41 °F) in winter. As a result of its northerly latitude and proximity to the Arctic Circle, the islands experience perpetual civil twilight during summer nights and very short winter days. The capital and largest city, Tórshavn, receives the fewest hours of sunshine of any city in the world at a mere 840 per year.

While archaeological evidence points to earlier human habitation, Færeyinga Saga and the writings of Dicuil place initial Norse settlement in the early 9th century. As with the subsequent Settlement of Iceland, the islands were mainly settled by Norwegians and Norse-Gaels, who additionally brought thralls (i.e. slaves or serfs) of Gaelic origin. Following the introduction of Christianity by Sigmundur Brestisson, the islands came under Norwegian rule in the early 11th century. The Faroe Islands followed Norway's integration into the Kalmar Union in 1397, and came under de facto Danish rule following that union's dissolution in 1523. The islands were formally ceded to Denmark, along with Iceland and Greenland in 1814 by the Treaty of Kiel. Following the establishment of an official Faroese orthography by Vencesclaus Ulricus Hammershaimb, the Faroese language conflict saw Danish being gradually displaced by Faroese as the language of the church, public education and law in the first half of the 20th century. The islands were occupied by the British during the Second World War, who refrained from governing Faroese internal affairs: inspired by this period of relative self-government and the declaration of Iceland as a republic in 1944, the islands held a referendum in 1946 that resulted in a narrow majority for independence. The results were annulled by Christian X, and subsequent negotiations led to the Faroe Islands being granted home rule in 1948.

While remaining part of the Kingdom of Denmark to this day, the Faroe Islands have extensive autonomy and control most areas apart from military defence, policing, justice and currency, with partial control over its foreign affairs. Because the Faroe Islands are not part of the same customs area as Denmark, they have an independent trade policy and are able to establish their own trade agreements with other states. The islands have an extensive bilateral free trade agreement with Iceland, known as the Hoyvík Agreement. In the Nordic Council, they are represented as part of the Danish delegation. In certain sports, the Faroe Islands field their own national teams. They did not become a part of the European Economic Community in 1973, instead keeping autonomy over their own fishing waters; as a result, the Faroe Islands are not a part of the European Union today. The Løgting, though suspended from 1816 to 1852, holds a claim as one of the oldest continuously-running parliaments in the world.

One Faroe Islander, Niels Ryberg Finsen, has won a Nobel Prize; due to the country's small population, the Faroe Islands resultingly hold the most Nobel laureates per capita.