In this book, the author gives a good bird's-eye view of the 1400 year history of Islam. This is such a complex subject that it cannot be condensed in anything more than just a bird's-eye view in a mere 200 pages. However, it's a good place to start. Most Americans tend to view Islam and the Middle East through the prism of the last 30 years, or maybe just since 9-11. One of the group members commented that High School textbooks in the 1960's devoted just a handful of pages to the Islamic world. Going forward into a future where our society will be engaging more closely with the Islamic culture, both as neighbors across the ocean and neighbors down the street, we have to do better at understand each others' perspectives. Armstrong's book gives a good start, not because everyone will agree with her perspective, but because there are few other books that tell the 1400 year story so concisely.
That being said, the book is sometimes hard to follow because of the rapid-fire names and philosophies, and "isms" that are thrown at the reader. For me anyway, I came away better understanding the larger themes of Islamic history rather than the details from this book.
Here are a couple of more books that I'd recommend after reading this one for the big picture:
The Crisis of Islam and What Went Wrong. The Clash of Islam with Modernity both by Bernard Lewis.
A Peace to End All Peace by David Frompkin is by far (in my opinion anyway) the best book describing the details of WW1 in the Middle East, and the carving up of it afterwards by England and France.