Are you looking primarily for religious, economic, military, political, or social history? Or some combination of some/all of those?

Edit: Also, are you interested in a specific geographical region? It is the rare text that tries to cover all this in toto--it's easier if you have a specific focus on Ottoman Empire/Turkey, Middle East (even better if you know if your focus in Levant or Gulf, etc...), North Africa, Andalusia...the histories, while interrelated, are also often distinct on important points.

I'd suggest A History of the Arab Peoples by Albert Hourani.

"Brief History of the Late Ottoman Empire" by M Sukru Hanioglu Has one good chapter on how Iraq, Jordan and Egypt became independent after World War One anad the demise of the Ottoman Empire.
Another book from the AskHistorians book list (see side bar, it's in the Resources section) is the book "Colonizing Egypt" by Tim Mitchell. It looks at Cairo from the middle of the nineteenth century up to the end of the Cold War, but before George HW Bush fought the first Persian Gulf war with Saddam Hussein. Egypt was a weird quasi colony and quasi independent nation, led by the Khedive of Egypt. They had closer contact with Great Britain and France than other Arab nations. This book focuses tightly on Cairo, which has ancient universities, important mosques and became an important center for producing Arab language movies and television programs. Cairo did not become an important city until after Islam entered Egypt and the process of Arabization began.