A square dance is a dance for four couples, or eight dancers in total, arranged in a square, with one couple on each side, facing the middle of the square. Square dances are part of a broad spectrum of dances known by various names: country dances, traditional dances, folk dances, barn dances, ceilidh dances, contra dances, Playford dances, etc. These dances appear in over 100 different formations, of which the Square and the Longways Set are by far the most popular formations.
Modern Appalachian square dancing
A square dance in Montreal, Quebec in 1941
Quadrille variation involving five couples dancing at a Colonial Ball in the Albert Hall, Canberra September 2016 (sepia)
American-style square dancers performing outdoors in Schleswig-Holstein, Germany in 2014
A country dance is any of a very large number of social dances of a type that originated in the British Isles; it is the repeated execution of a predefined sequence of figures, carefully designed to fit a fixed length of music, performed by a group of people, usually in couples, in one or more sets. The figures involve interaction with your partner and/or with other dancers, usually with a progression so that you dance with everyone in your set. It is common in modern times to have a "caller" who teaches the dance and then calls the figures as you dance. Country dances are done in many different styles.
Comical 18th-century country dance; engraving by Hogarth
Village country dance; engraving by Abraham Bosse, 1633
Lorin's contradanse choreography, one of the earliest western dance notations
The "La Trénis" figure of the Contredanse, an illustration from Le Bon Genre, Paris, 1805