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There are a LOT of books on African hunting - your tastes may vary from mine but here are some from my own library:

Steward Edward White wrote a number of good books, including Lions in the Path, The Rediscovered Country, African Camp Fires, and The Land of Foot Prints.
John "Pondoro" Taylor's classics African Rifles and Cartridges and Pondoro: Last of the Ivory Hunters are great reads.
The W.D.M Bell books (Bell of Africa, Karamojo Safari, Wanderings of an Elephant Hunter) are classics.
A Hunter's Wanderings in Africa by Frederick Courtney Selous is worthwhile, but Selous wasn't the most entertaining writer.
Channing Beebe's book Cannibals and Big Game is OK.

Those are from the Africa of yesteryear.

More recent book are Ron Thompson's The Adventures of Shadrek (Shadrek was a poacher) and Mahohboh.
Bruce Kinloch's book The Shamba Raiders relates African game management from the viewpoint of a game warden.
Craig Boddington has written some OK books, the best of which is Safari Rifles, which is complemented by Gregor Woods' Rifles for Africa and and Robertson's The Perfect Shot.

And no list would be complete without Mellon's African Hunter.