The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides. The narrator is a square named A Square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. The first half of the story goes through the practicalities of existing in a two-dimensional universe as well as a history leading up to the year 1999 on the eve of the 3rd Millennium.