The exhibition on the lower floor of Gilsstofa is dedicated to the Briem family. It was Eggert Ólafur Briem (1811–1894), a district commissioner, who had Gilsstofa built. The rooms are furnished to resemble a well-appointed parlor and office from the mid-19th century, featuring family portraits and information about Eggert, his wife Ingibjörg Eiríksdóttir Briem (1827–1890), and their 19 children.