I would recommend you start out with some primers on the history of Islam. Karen Armstrong's Islam: A Short History would be a great option, but there are others. Your local library probably has some books on the subject.

For more in-depth info on what is going on today and the background check out the works of Bernhard Lewis, he is one of the leading authors on this subject. There is one book from the late 60s by him that is practically a must-read for any scholar in the field, sadly I cannot remember the title at the moment.

Thomas Friedmans book From Beirut to Jerusalem is another great classic, starting with the Lebanese Civil war from 1975, the invasion of Lebanon by Israeli forces in 1982 and the first Intifada in the late 1980s up to the very early 1990s. It is a bit sad that the narration stops there, but it is still a great resource on understanding the dynamics of the region. Note that the book assumes that you are somewhat familar with the events described, it is aimed at an audience who grew up watching the Lebanese civil war and the Antifada in the news on tv and has some understanding of Israeli history. My tip is to read this book with a tablet, phone or at least pen and paper next to you so that you can easily look stuff up. I found it worthwhile to take notes and write down questions, there are a lot of things that Friedman touches with an off-the-cuff remark and that left me utterly confused the first time I read the book. I appreciated his book far more once I had gained some additional knowledge on the region and read it a fourth and fifth time.