The Qu'ran or Koran is the sacred text of Islam, analogous to the Bible in connection with Christianity or the Tanakh with Judaism.
The book builds on established Judeo-Christian stories, expanding on many of them. Additionally, some native mythology is also mixed in. For example, Djinns often take the place of demons in this book.
The fall of Sheytan (the devil) is a bit different. What happened was that when Adam and Eve were created, he refused to bow down to the inferior creatures, and became the devil. Sheytan is also a genie instead of a fallen angel as in Christian mythology.
Part copied from Liberapedia