Alrighty, let's start. Denmark is the southernmost Scandinavian country, with a population of about 5 million. It is made up of the Jutland peninsula and numerous island, on the biggest of which is the capital, Copenhagen (Koebenhavn in Danish).
Between the 9th and 11th centuries, Danish Vikings invaded most of Western Europe as far as North Africa, were the only invaders to take Paris since Franks and until the Germans in 1940. A group of those Vikings invaded Northern England and created the so-called "Danelaw". Some Danish kings became king of England, e.g. Canute the Great in the early 11th century. Another group of Danes were granted the land of Normandy by the king of France, and later invaded England, and the descendants of those Danes are still on the throne of England (and with the intermarriages, all European monarchies) nowadays. The Danes ruled over the south of Italy for about 100 years (and left their genes in the local population, so that there are still blue-eyed Sicilians nowadays).
Denmark later ruled over all Scandinavia (Sweden, Norway, Faroe Islands, Iceland, Greenland), and still retain their sovereignty over the Faroe Islands an Greenland.
Many Danish people nowadays have surnames ending in "-sen" (eg. Andersen, Nielsen, Rasmusen...). Denmark, like Sweden and Norway, has a disproportionately high number of Nobel prize winners and Olympic medals (both summer and winter). Although Denmrk is a EU member, it still uses the Crown instead of the Euro, like other Scandinavian countries.
Denmark is a very egalitarian society, and women enjoy more equality with men than in almost any other country (except maybe Sweden and Norway).
Danish language is a North Germanic language, descedning from Old Norse.
Famous Danish companies include Lego and Bang & Olufsen. Denmark also has the highest
rate of strikes in the world.