Rhuidean is a city in the Aiel Waste. It was built in a valley near the mountain Chaendaer by the Jenn Aiel, and all but abandoned for many years. Aiel clan chiefs could enter it once, to learn their people's history through a gigantic ter'angreal made of a number of crystal columns; Aiel Wise Ones entered it twice.
In Rand's struggle with Asmodean at the end of The Shadow Rising, many of the buildings in Rhuidean have been destroyed or damaged. Avendesora was badly burned, but survived. One end of the valley has been flooded into a huge lake.
At the beginning of The Fires of Heaven, Rand al'Thor has reopened Rhuidean to the Aiel. Moiraine has enlisted Hadnan Kadere's caravan to move at least some of the ter'angreal out of the city, on the way to Tar Valon. Rand restored the fountains of Rhuidean to working order before leaving the city in FOH 7.