I recently read (and loved) John Iliffe’s Africans. Iliffe is a professor at Cambridge, and has been a leader in understanding African society on their own terms for decades now. Because so much of the continent did not keep written records, narrative histories inevitably rely on outsider accounts. That’s why books like Martin Meredith’s (which I really dislike) are so name heavy, either discussing the colonists or the elite they recorded their interaction with. Iliffe, on the other hand, brings in archaeology, linguistics, genetics, anthropology, and economics to show what was almost certainly happening prior to European contact. His 13 chapters are temporal and thematic: like the “impact of metals” (maybe equivalent to the European Bronze/Iron/Medieval Age, but he does not allow European chronology to impinge on Africa), “Christianity and Islam” (the literate traditions that accompanied state building c. 500-1500), and so on.

The book also rocks because it basically is a 1000 1-paragraph synthetic (drawing from other historians) essays, so if you want to follow up on anything you can just go to his bibliography/footnotes, but also you are safe knowing that his account is basically a good mainstream summary of the research c. its publication, especially once you take into an account his thesis/bias (that Africans have been remarkably successful given their historical struggle with underpopulation).

If there’s something more specific you are interested in (like West Africa, Egypt, etc.) I’m happy to help, but I just wish someone told me sooner about this specific book.