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The following titles, all by working physicists, attempt to communicate quantum theory to lay people, using a minimum of technical apparatus.
Chester, Marvin (1987) Primer of Quantum Mechanics. John Wiley. ISBN 0-486-42878-8
Cox, Brian; Forshaw, Jeff (2011). The Quantum Universe: Everything That Can Happen Does Happen:. Allen Lane. ISBN 1-84614-432-9.
Richard Feynman, 1985. QED: The Strange Theory of Light and Matter, Princeton University Press. ISBN 0-691-08388-6. Four elementary lectures on quantum electrodynamics and quantum field theory, yet containing many insights for the expert.
Ghirardi, GianCarlo, 2004. Sneaking a Look at God's Cards, Gerald Malsbary, trans. Princeton Univ. Press. The most technical of the works cited here. Passages using algebra, trigonometry, and bra–ket notation can be passed over on a first reading.
N. David Mermin, 1990, "Spooky actions at a distance: mysteries of the QT" in his Boojums all the way through. Cambridge University Press: 110-76.
Victor Stenger, 2000. Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Buffalo NY: Prometheus Books. Chpts. 5-8. Includes cosmological and philosophical considerations.
More technical:
Bryce DeWitt, R. Neill Graham, eds., 1973. The Many-Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, Princeton University Press. ISBN 0-691-08131-X
Dirac, P. A. M. (1930). The Principles of Quantum Mechanics. ISBN 0-19-852011-5.  The beginning chapters make up a very clear and comprehensible introduction.
Hugh Everett, 1957, "Relative State Formulation of Quantum Mechanics", Reviews of Modern Physics 29: 454-62.
Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (1965). The Feynman Lectures on Physics. 1–3. Addison-Wesley. ISBN 0-7382-0008-5.
Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-111892-7. OCLC 40251748.  A standard undergraduate text.
Max Jammer, 1966. The Conceptual Development of Quantum Mechanics. McGraw Hill.
Hagen Kleinert, 2004. Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. Singapore: World Scientific. Draft of 4th edition.
Gunther Ludwig, 1968. Wave Mechanics. London: Pergamon Press. ISBN 0-08-203204-1
George Mackey (2004). The mathematical foundations of quantum mechanics. Dover Publications. ISBN 0-486-43517-2.
Albert Messiah, 1966. Quantum Mechanics (Vol. I), English translation from French by G. M. Temmer. North Holland, John Wiley & Sons. Cf. chpt. IV, section III.
Omnès, Roland (1999). Understanding Quantum Mechanics. Princeton University Press. ISBN 0-691-00435-8. OCLC 39849482.
Scerri, Eric R., 2006. The Periodic Table: Its Story and Its Significance. Oxford University Press. Considers the extent to which chemistry and the periodic system have been reduced to quantum mechanics. ISBN 0-19-530573-6
Transnational College of Lex (1996). What is Quantum Mechanics? A Physics Adventure. Language Research Foundation, Boston. ISBN 0-9643504-1-6. OCLC 34661512.
von Neumann, John (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press. ISBN 0-691-02893-1.
Hermann Weyl, 1950. The Theory of Groups and Quantum Mechanics, Dover Publications.
D. Greenberger, K. Hentschel, F. Weinert, eds., 2009. Compendium of quantum physics, Concepts, experiments, history and philosophy, Springer-Verlag, Berlin, Heidelberg.