I hope this question is appropriate for this forum. I am compiling a list of all books about the Riemann Hypothesis and Riemann's Zeta Function. Here is my list:
The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller (Eds.)
The Riemann Hypothesis and Hilbert's Tenth Problem, by S. Chowla
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, by John Derbyshire
The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, by Marcus du Sautoy
Riemann's Zeta Function, by Harold M. Edwards
The Riemann Zeta-Function: Theory and Applications, by Aleksandar Ivic
The Riemann Zeta-Function, by Anatoly A. Karatsuba and S. M. Voronin
In Search of the Riemann Zeros, by Michel L. Lapidus
Limit Theorems for the Riemann Zeta-Function, by Antanas Laurincikas
The Lerch zeta-function, by Antanas Laurincikas and Ramunas Garunkstis
Spectral Theory of the Riemann Zeta-Function, by Yoichi Motohashi
An Introduction to the Theory of the Riemann Zeta-Function, by S. J. Patterson
Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers, by Dan Rockmore
The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics, by Karl Sabbagh
Seminar on the Riemann Zeta Function 1965-1966, by Robert Spira
Zeta and q-Zeta Functions and Associated Series and Integrals, by H. M. Srivastava and Junesang Choi
The Theory of the Riemann Zeta-Function, by E. C. Titchmarsh, D. R. Heath-Brown (Ed.)
Zeta Functions over Zeros of Zeta Functions, by André Voros
Are any books missing from my list? I don't include books by mathematical cranks (especially books by amateurs who claim to prove RH in their book). I also don't include books about analytic number theory in general that include some material about the Riemann Hypothesis or Riemann's Zeta Function. I did not include books about related topics, such as zeta functions of groups. I realize that one could quibble about the inclusion of some of the books on my list, such as Laurincikas's book about the Lerch Zeta Function. I would be very grateful for any additions to my list.
Edit: Excluding books that consist of collections of mathematical tables, and books that are paper-length (say, under 50 pages), the following books can be added to my list:
Bernoulli Numbers and Zeta Functions, by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko, and Don B. Zagier, Springer (June 30, 2014), 274 pp.
Ramanujan Lecture Notes Series, Vol. 2: The Riemann zeta function and related themes (Proceedings of the international conference held at the National Institute of Advanced Studies, Bangalore, December 2003), R. Balasubramanian, K. Srinivas (Eds.), 206 pp.
Lectures on the Riemann zeta-function (1962), by K. Chandrasekharan, 148 pp.
The Bloch-Kato Conjecture for the Riemann Zeta Function, John Coates, A. Raghuram, Anupam Saikia, R. Sujatha (Eds.), London Mathematical Society Lecture Note Series (Book 418), Cambridge University Press (April 30, 2015), 320 pp.
Elizalde, Emilio, Ten Physical Applications of Spectral Zeta Functions, Lecture Notes in Physics 855, Springer, Berlin, 2012 (2nd edition), 290 pages
Gavrilov, N. I. Problema Rimana o raspredelenii korneidzetafunktsii. (Russian) [The Riemann problem on the distribution of the roots of the zeta function ] Izdat. L'vov. Univ., Lvov, 1970 1970 172 pp.
Ivic, A. Lectures on mean values of the Riemann zeta function. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 82. Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1991. viii+363 pp. ISBN: 3-540-54748-7
Ivic, A. The Theory of Hardy's Z-function. Cambridge Tracts in Mathematics 196. Cambridge: Cambridge University Press. ISBN 978-1-107-02883-8, 264 pages, 2012
Ivic, A. Topics in recent zeta function theory. Publ. Math. d'Orsay, Université de Paris-Sud, Dép. de Mathématique, 1983, 272 pages
Lectures on the Riemann Zeta Function, by H. Iwaniec, American Mathematical Society (October 30, 2014), 119 pp.
Contributions to the Theory of Zeta-Functions: The Modular Relation Supremacy, by Shigeru Kanemitsu and Haruo Tsukada, World Scientific Publishing Company (June 30, 2014), 280 pp.
Random Matrices, Frobenius Eigenvalues, and Monodromy, by Nicholas M. Katz and Peter Sarnak, American Mathematical Society (November 24, 1998), 419 pp.
Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, by Michel L. Lapidus and Machiel van Frankenhuysen, 1999
Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings, by Michel L. Lapidus and Machiel van Frankenhuysen, 2006
Ramachandra, K. On the mean-value and omega-theorems for the Riemann zeta-function. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 85. Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1995. xiv+169 pp. ISBN: 3-540-58437-4
History of Zeta Functions, by Robert Spira, 3 volumes, 1218 pages, 1999
New Directions in Value-distribution Theory of Zeta and L-functions: Wurzburg Conference, October 6-10, 2008 (Berichte aus der Mathematik), Rasa Steuding, Jörn Steuding (Eds.), Shaker Verlag GmbH, Germany (December 31, 2009), 346 pp.
Van der Veen, Roland; van de Craats, Jan De Riemann-hypothese. (Dutch) [The Riemann hypothesis] Een miljoenenprobleem. [A million dollar problem] Epsilon Uitgaven, Utrecht, 2011. vi+102 pp. ISBN: 978-90-5041-126-4
Van Frankenhuijsen, Machiel, The Riemann Hypothesis for Function Fields: Frobenius Flow and Shift Operators, London Mathematical Society Student Texts (Book 80), Cambridge University Press (January 9, 2014), 162 pp.