Iceland’s first parliament, the Alþingi, was created at Þingvellir in AD 930. After losing its independence in the 13th century, the country gradually won back its autonomy, and the modern Alþingi moved into this current basalt building in 1881; a stylish glass-and-stone annexe was completed in 2002. Visitors can attend sessions (four times weekly mid-September to early June; see website for details) when parliament is sitting.