Two recommendations that have been invaluable for me:

i) Fred Cooper, Africa Since 1940: Less detailed than Meredith's book, Cooper focuses more on the themes that have pervaded African politics and development over the past 70 years. He does use case studies to highlight specific points and overall is a fantastic book. Also highlights the internationalism that has helped shape Africa, and regularly ignores national borders in favour of transnational ideas and exchanges. Highly recommended.

ii) Martin Meredith, The State of Africa: It is a relatively detailed history of the entire continent and designed for general readers more than academics. It isn't without its flaws (it can be rather Eurocentric in places) but it is still a good book.

If you want anything more specific, do let me know.