Ask your tutor for a bibliography, I'm sure they'll be happy (delighted) that you want to do some preliminary reading before the course begins, and most tutors will have prepared one for the course anyway.

I'm pretty sure I've found the course you're referring to (if you search the title of the course it's the only one).

Although the title of the course says "earliest times" it actually looks like it focuses on the past few centuries.

I always find myself recommending the same few books on this sub, at least for general single volume histories of the region, because they are quite good. The Arabs: A History by Eugene Rogan and Western Imperialism in the Middle East: 1914-1958 by D.K. Fieldhouse. In two volumes, Malcolm Yapp's Making of the Modern Near East: 1792 - 1923 and The Near East since the First World War are also fantastic.

There are other, more country specific, books I could point you to but for what looks to be a survey course those should definitely set you on the right path. It might be worth seeking out something specifically on Israel/Palestine just because it's such a "sudden" issue. I quite like Tom Segev's "One Palestine, Complete" but both of the previous books I mentioned also cover Zionism and the foundation of Israel to a certain extent. I'm also an Egypt nerd so I quote like P.J. Vatikiotis' "History of Modern Egypt: From Muhammad Ali to Mubarak."

If you want a much longer work that truly is from "the earliest times" then maybe Hodgson's The Venture of Islam or Hourani's History of the Arab Peoples. The latter is a "classic" but I found it to be impossibly dry.

Unfortunately anything on the pre-Arab conquests (i.e. Antique roman or biblical Middle East) is outside my area of knowledge, but again, it looks like your course isn't really about that despite the title.

I think these books are good for overview

http://www.amazon.com/The-Middle-East-Brief-History/dp/0684832801

http://www.amazon.com/History-Middle-East-Fourth-Edition/dp/0143121901