Give me books.

Gabe at A Handful of Sand highlights an aspect of reading that many of us encounter: the frequent realization that one is utterly ignorant of the history or background of an entire field of human knowledge or history. The historical novels I love do this most often; Vikram Seth's A Suitable Boy left me craving to know more about both twentieth century India and its long history. Watership Down led me to read more about rabbits. The lush narrative at the beginning of Middlesex revealed my ignorance of modern Turkish history (Smyrna burned?). This can lead to two outcomes:

-Lazy acceptance of whatever potentially dubious factoids and accounts of the historical experience or state of technology the book provides. Alternatively, failure to believe in some of the author's more unusual devices (Van Eck phreaking is real? I had no idea).
-Ransacking of library to find something to slake your thirst for something more substantive.

I tend toward the former, but only because I have limited time to sort through the field to separate the trash history and junk scholarship from the good stuff. I am in the market for a few good single volume histories at this time. An example of what I am looking for is The Fatal Shore, a book I picked up when I realized that no class I had ever taken mentioned the settling of Australia and its neighbors by the British.

Can anyone recommend a good history of India (20th c. or pre-colonial), 20th c. South America, the medieval Arab empire, or post-colonial Africa? Giant tomes are okay, but ideally I want something they could assign in a college survey course but which is not too dry.