I'm only an undergraduate myself and can't give detailed descriptions, but I'd recommend the book by Maria Rosa Menocal "Ornament of the World: How Muslims, Jews, and Christians Created a Culture of Tolerance in Medieval Spain." New York: Little, Brown and Company, 2002.

It's about Al-Andalus (The common name for Muslim Spain) but its opening chapters discuss what led the Umayyad dynasty to flee Damascus for Al-Andalus. It then covers the next few centuries of the history of Al-Andalus, with quite a few mentions of events in the greater Muslim world as well.

For a while after fleeing, the Umayyads remained an Emirate in Al-Andalus, nominally loyal to the newly crowned Abbasid power in Baghdad--the Abbasids moved the capitol from Damascus to Baghdad shortly after gaining power. Damascus was reminiscent of the old, and so the Abbasids decided to leave it. Eventually, the Umayyads declared a caliphate themselves and ruled for a few hundred years until internal strife and constant foreign attacks led their caliphate to slowly fall apart.

Menocal has a number of other books on the subject. The overall context of the Arab world is also described well in Albert Hourani's "A History of the Arab Peoples." Cambridge: Harvard University Press, 1991.

Hope it helps at least a bit!

That's a very long history but is there a specific thing you want to know?