These are all the books I am aware of that meet the criteria I set:
This list is available as a BibTeX bibliography file which can be downloaded from: https://drive.google.com/file/d/0B-yLrQYDVquBc0VsMEp2c1FMRDg/view?usp=sharing
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.
The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller (Eds.), Springer, 2008
Lectures on the Riemann zeta-function, by K. Chandrasekharan, Tata Institute of Fundamental Research, 1953, 148 pp.
The Riemann Hypothesis and Hilbert's Tenth Problem, by S. Chowla, Gordon and Breach, Science Publishers, Ltd., 1965
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.
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, by John Derbyshire, Joseph Henry Press, 2003
The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, by Marcus du Sautoy, HarperCollins, 2003
Riemann's Zeta Function, by Harold M. Edwards, Academic Press, 1974
Elizalde, Emilio, Ten Physical Applications of Spectral Zeta Functions, Lecture Notes in Physics 855, Springer, Berlin, 2012 (2nd edition), 290 pages
Gál, István Sándor, Lectures on algebraic and analytic number theory; with special emphasis on the theory of the Zeta functions of number fields and function fields, Jones Letter Service, Minneapolis, 1961, 453 pp.
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.
The Mysteries of the Real Prime, by M.J. Shai Haran, London Mathematical Society (December 6, 2001), 256 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
The Riemann Zeta-Function: Theory and Applications, by Aleksandar Ivic, John Wiley & Sons, Inc., 1985
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.
The Riemann Zeta-Function, by Anatoly A. Karatsuba and S. M. Voronin, Walter de Gruyter & Co., 1992
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, Birkhäuser, 1999
Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings, by Michel L. Lapidus and Machiel van Frankenhuysen, Springer, 2006
In Search of the Riemann Zeros: Strings, Fractal Membranes, and Noncommutative Spacetimes, by Michel L. Lapidus, American Mathematical Society, 2008
Limit Theorems for the Riemann Zeta-Function, by Antanas Laurincikas, Kluwer Academic Publishers, 1996
The Lerch zeta-function, by Antanas Laurincikas and Ramunas Garunkstis, Kluwer Academic Publishers, 2002
Prime Numbers and the Riemann Hypothesis, by Barry Mazur and William Stein, Cambridge University Press (October 31, 2015), 150 pp.
Spectral Theory of the Riemann Zeta-Function, by Yoichi Motohashi, Cambridge University Press, 1997
An Introduction to the Theory of the Riemann Zeta-Function, by S. J. Patterson, Cambridge University Press, 1988
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
The Theory of the Hurwitz Zeta Function of the Second Variable, by Vivek V. Rane, Alpha Science International Ltd (December 31, 2015), 300 pp.
Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers, by Dan Rockmore, Random House, Inc., 2005
The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics, by Karl Sabbagh, Farrar, Straus, and Giroux, 2002
History of Zeta Functions, by Robert Spira, 3 volumes, Quartz Press (392 Taylor Street, Ashland OR 97520-3058), 1218 pages, 1999, ISBN 0-911455-10-8
Seminar on the Riemann Zeta Function 1965-1966, by Robert Spira, Mimeographed typescript, University of Tennessee, Knoxville, 57 pages
Zeta and q-Zeta Functions and Associated Series and Integrals, by H. M. Srivastava and Junesang Choi, Elsevier Inc., 2012
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.
Zeta and eta functions: A new hypothesis, by Ashwani Kumar Thukral, CreateSpace Independent Publishing Platform (December 17, 2015), 56 pp.
The Theory of the Riemann Zeta-Function, by E. C. Titchmarsh, D. R. Heath-Brown (Ed.), Second edition, Oxford University Press, 1986
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
The Riemann Hypothesis, by Roland van der Veen and Jan van de Craats, The Mathematical Association of America (January 6, 2016), 154 pp.
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.
Zeta Functions over Zeros of Zeta Functions, by André Voros, Springer-Verlag, 2010