1. Men of Mathematics (E.T. Bell, 1937)
2. The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike (Peter Borwein et.al, 2007)
3. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (John Derbyshire, 2004)
4. Unknown Quantity: A Real and Imaginary History of Algebra (John Derbyshire, 2007)
5. Journey through Genius: The Great Theorems of Mathematics (William Dunham, 1991)
6. Riemann’s Zeta Function (H. M. Edwards, 1971)
7. Gamma: Exploring Euler’s Constant (Julian Havil, 2009)
8. The Man Who Loved Only Numbers (Paul Hoffman, 1999)
9. The Riemann Zeta-Function: Theory and Applications. (Alexander Ivic, 2004)
10. e: The Story of a Number (Eli Maor, 2009)
11. An Imaginary Tale: The Story of √-1 (Paul J. Nahin; 1998)
12. Dr. Euler’s Fabulous Formula (Paul J. Nahin; 2006)
13. Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers (Dan Rockmore, 2006)
14. Infinity and the Mind (Rudy Rucker, 2004)
15. The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics (Karl Sabbagh, 2004)
16. The Prime Numbers and Their Distribution. (Tenenbaum and Mendès, 2000)
https://books.google.ca/books/about/Riemann_s_Zeta_Function....
This is most obvious in the naming of the J function near the bottom, which I have not seen anywhere else. Riemann originally called that function a generic f.
At any rate, Edwards' book is great because it develops the theory from a historical viewpoint. It begins with a very well-annotated exposition of Riemann's original paper and the rest of the book goes on to explain other mathematicians' successive results in filling in all of the gaps that Riemann left in his paper. I recommend this book to any serious student of zeta.