The Royal Swedish Academy of Sciences built this hilltop observatory in the late 1740s. Now a museum dedicated to science, it's open for guided tours of the observation rooms and the 18th-century instruments of Pehr Wargentin, an astronomer and statistician who lived and worked here for 30 years. The guide describes how scientists tried to solve the pressing problems of their day, from calculating the distances between planets, to determining navigational longitude at sea. A narrow staircase leads to the dome, where you get a wonderful, unobstructed view of the Stockholm skyline. This is one of the city's lesser-known museums, but it is well worth a visit. On Tuesday evenings between October and March, you can stargaze through the museum's early 20th-century telescope.