When Baghdad Ruled the Muslim World by Hugh Kennedy is a well-written and entertaining history of the Abbasid caliphs, who ruled the Muslim world for about 200 years from AD 762. This period is often referred to as the Golden Era of the Islamic empire, where poetry and science flourished, and their wealth seemed endless.
One of the things I liked most about the book was its extensive use of original sources. The author uses a number of writings from Arabian historians from that era, which provides insight on how the events of the day were perceived. When a caliph dies early in his reign (which happened a lot!), the author is often able to indicate whether the death was suspicious or just bad luck.
While the material can be a little tough at times (particularly when it comes to names of the caliphs, which appear to all start with the letter 'M', and which often changed when they took the position), the author does an excellent job of keeping things moving, with many stories and amusing anecdotes.