It's a good book, though pretty brief in parts. It makes an OK introduction, though, for precisely that reason.
A more significant complaint might be that it's not objective. There is a distinctive thread running through Armstrong's work, which is her belief that the "true" form of any religion is compassionate, humanist, based on some flavor of the Golden Rule. As such, she simply rejects most forms of fundamentalism, or any religious view that is particularly rigid, oppressive, or violent. That's certainly present here. It's not a neutral view of religion, though, and it's not one that everyone shares. On the other hand, the firmness of her conviction provides Armstrong with a good vantage point from which to elucidate what she calls the "symbiotic relationship" between fundamentalism and "coercive secularism." I found that insight quite thought provoking and valuable, and so I'm more than happy to work through her subjective viewpoint. Nor do I think there would be much value in her qualifying or disclaiming her non-objective sense of religion. All of which is to say, it works for me.
So I enjoyed the book—the third I've read from this author—and I'll probably take a look at A Short History of Myth as well. But I'll also be looking for a more in-depth introduction to Islam, because this one was a little on the compact side.