Muhammad is believed to have flown to Jerusalem on a magical night journey by riding on the back of buraq. The Qur'an talks about the night journey of God's servant (it isn't clear it means Muhammad, some say it refers to Moses), but says almost nothing about it, and doesn't mention any magical animals or anything.
In the earliest Islamic sources that explain this journey, Muhammad is said to have ridden on buraq, which is described as a sort of whitish magical steed. This later became understood as a bizarre magical Middle Eastern chimera with a human head. Here's some examples (from Persian tradition, which didn't have the violent anti-image ideology that gradually took over Islam).
