Patricia Crone wrote this in 1980, adapting it from the first part of her PhD thesis. (Another part became the book "Roman, Provincial and Islamic Law" - as of 1997, this has been challenged and as far as I know, Crone has abandoned it.) Anyway "Slaves on Horses" is the first work of Crone's which I can recommend.
Her earlier work relied on "Islam as others saw it", to borrow a phrase. This work assumes the barest skeleton of the "Hagarism" narrative, and fleshes out that skeleton from the historical Muslim accounts mainly from hadith and administrative records. The book seeks to explain how and why the Caliphate ended up reliant upon "slaves on horses" to defend it. After all, the phrase "slaves on horses" is a phrase of horror in Jewish and Christian literature; and Islamic apocalyptic complains about it too.
As such this is best termed a military and caste history, from the 650s on. Crone finds the evolution of the Caliphal armies to be explicable by practical concerns, not religious. As a result she has little of Islam-as-religion in here, excepting the propaganda from this or that rebel.
It is less a "book" than an 80-something-page monograph, with extensive appendices. The appendices are the important part: they tell you who was stationed where and when, and of what family and tribe... in Syria and Iraq. (Egypt and North Africa and Spain do not feature.) These appendices are still of value for those who are fact-checking hadiths of the Fertile Crescent. They are in this book to show how Sufyani administration differed from Marwani administration which, in turn, differed from `Abbasi administration.
The writing style is breathless and endnote-reliant - typical of Crone's earlier work - and you can be lulled into reading quickly past many pages before realising that you have not followed the argument. The book's argument is, however, solid; you just have to work harder at it to absorb it. The book has held up over time; I have not found in the literature debunkings on the scale as, say, Crone's OWN debunking of her "Meccan Trade" in "Quraysh and the Roman Army".