This chapter comes from their book discussing the archaeological, anthropological and historical evidence available for the study of the relationships between the early Islamic society and state and the "origins of Europe." The title of the book comes from the title of Pirenne's classic study, Mohammad and Charlemagne in which he argued [many decades ago] that Europe as we know it was able to "become" largely as unintended results of the rise of Islam far to the East. Pirenne's view has long been viewed by historians as "nutty"; however, recent study, using source materials unavailable to earlier historians [indeed to Pirenne too], argues for some validity to his thesis.
In order to understand this piece, you need to remind yourself of the geography of Europe and the Middle East; including Eastern Europe, Scandinavia, Russia, and to remember what you learned earlier about Vikings, the origins of Slavic settlement in Eastern Europe, the origins of East European states in the early middle ages.
What is the evidence that these authors provide about early Baghdad and the origins of the Abbasid Caliphate?