Unfortunately, the monography Islamic History as Global History by Richard Eaton seems to be out of print. However, if you can get a used copy, I highly recommend it a good, short (46 pages) introduction to Islamic civilizations as part of global historical processes. While not a true introduction to Islam, it is not meant for a specialized reading audience either. Two passages that leapt out at me are below. Thanks to miamvi for the introduction.
Where India is concerned, two lines of historical inquiry are discernible, one of them intellectual, the other social. The former consists of efforts to unravel the complex and fascinating ways that Muslims hailing from points to the west came to grips intellectually with India’s highly developed Hindu-Buddhist systems of religion and thought. Arab rule in eighth-century Sind having weakened and died, it was left to Persianized Turks to establish a permanent Muslim presence in India from the thirteenth century. But what would the new ruling class, itself only recently converted to Islam in Central Asia, make of the land of the Buddha, Shiva, and the marvelous incarnations of Vishnu? And to what extent would Islam adapt or change in order to find for itself a niche in India’s rich cultural universe? Lurking behind these apparently innocent question were fundamental issues, both for modern historians looking back over the past seven centuries and for Indian Muslims living in any one of them. In its manifold accommodation with India’s culture, was Islam becoming diluted? Or was it simply growing with the times, adapting to new circumstances, building on what was already there? These were urgent questions, because in coming to terms with India’s formidable cultural legacy, Muslims were also compelled to come to terms with their own.
(pg. 34)
On Marco Polo and Ibn Battuta:
The two travelers differed most profoundly, however, in their relationship to the societies they visited. Marco Polo, who died in 1324, the year before Ibn Battuta embarked from Morocco, had been a stranger everywhere he went, and he knew it. Indeed, his fame derives from his having introduced Europe, which in the thirteenth century, was just emerging from being a global backwater, to a fabulous but utterly alien world of which it had only the haziest impressions. On the other hand, Ibn Battuta, in his intercontinental wanderings, moved through a single cultural universe in which he was utterly at home.… Overall, his book contains a self-assured tone in which the cultural unity of Dâr al-Islâm [House of Islam], from Spain to China, was not even an issue; it was simply taken for granted.
(pg. 44)