The oldest and only surviving waterwheel in Damascus is in As-Salhieh district on the slopes of Mount Qassiyoun. This water-raising device dates back to the Ayubid era and was designed by Badi' Al-Zaman Al Jazari
The waterwheel used to carry water from Yazid River to a 12-meter-high canal ending in the nearby Al-Bimaristan Al-Qaymari Hospital. It remained in use until the early 1970s. Many other waterwheels existed in the area, which is still known as Ziqaq Al-Nawa'ir (Alley of Waterwheels).
Update: My friend GottfriedStutz left some very informative comments about Al-Jazari.