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At home I have a nice dog-eared copy of Colin McEverdy's The Penguin Atlas of African History.
Of course Africa is a big place, and things developed fairly independantly north and south of the Sahara for most of its history. But if you are interested in the development all all African civilizations (From Bushman to Arab), this is the best resource I know of.
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Helen Tilley spent the better part of a decade investigating development in Africa, especially in relation to British Parliamentary funding of resource projects addressing issues like clean water, mosquitos and flooding. Her most recent book, Africa as a Living Laboratory: Empire, Development, and the Problem of Scientific Knowledge, 1870-1950, is a thoroughly-researched and well-written text.
Especially useful is the lengthy appendix providing primary source data taken from British Parliamentary Papers (take a look here).
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I think the Wikipedia article about Africa's history might be as good an entry point for your research as any other. It's mainly an overview which just shortly mentions the most important kingdoms and civilizations, but it has lots of links presumably (I didn't check them) leading to more detailed articles.
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Check out Burns and Collins's A History of Sub Saharan Africa, a general overview. It seemed to tell a lot of the same stories as an into to African History course I took.
John Reader's Africa: A Biography of the Continent was a bit more enjoyable, writing-wise. Still glad I read both for the variance in perspective.
I'd be curious to hear what problems you or other readers find in those books. I also wouldn't mind hearing of a good into book written outside of the US/Europe.