First of all this book is a great failure, from the point of view of who the author is. It is a shame that Crone was forced by Columbia University Press to write this kind of general survey. The book only repeats what has been know for more than 50 or 60 years. Scholars such as Laoust have already given us a much better account of these issues. In fact, one feels that this is almost a translation of Laoust's book. Importantly, there is no political theorizing in this work, only description.
This is really nothing but a basic and not so practical textbook that pretends to be scholarship. I hope Crone will use in a more scholarly way her position at the School of Advanced Studies. This is not the kind of book one expects from her.
This is a great treatment of Islamic political thought from the founding of Islam to the end of the medieval period. It is written with the standards of professional scholarship, with extensive documentation and references, and some interesting nuggets and arguments in the notes. However, I doubt this would limit the interest for a general audience, as the markings of scholarship are pretty unobtrusive.
Of course, one of the main reasons a general readership would care is to get some context and underpinnings for the political relationships that Westerners are becoming more and more interested in. _God's Rule_ does serve that purpose well. It also shows the dizzying variation in the political thought of various branches and sects of Islam. For theories of the obligations of the state; the proper legitimation of rulers; the relationship between state, society, and religion; the role of "civil disobedience" (to use an anachronistic term); the state and warfare; etc., Crone shows that Islam is incredibly mutable. That in itself is a valuable insight, as we think today about the possibilities for institutional change from autocracy in the Islamic world and the political arrangements that do exist.
Of course, the book is not written with an eye to current events, and it is also excellent as a treatment of the history of political thought in its own right. The time period covered includes an era in which an Islamic empire was the ascendant political unit in the world. More generally this is a large and politically important region of the world at the time. For these reasons its political thought compels our interest.
One minor complaint: I wish Crone had given more emphasis to the size of the various Islamic sects she surveys. Sometimes it is easy to forget that some of the individual communities covered were very small.
This would not make such a good introduction to the history of the Islamic world in general. _History of Islamic Societies_ by Ira Lapidus is a good place for something like that. But it would probably make an excellent 2nd or 3rd book for someone interested in Islamic history.