It is entirely possible to pass a graduate quantum mechanics course and have no view whatsoever on what the theory says the world is like. The formalism tells you how to compute probabilities; it does not tell you what happens during a measurement, or whether the wavefunction is a physical thing. That gap has a name — the measurement problem — and it is the whole subject here.
The reading trap is the gap in the middle of the literature. Popular books are excellent at conveying that something is strange, and then stop. The technical philosophy of physics assumes linear algebra, Hilbert spaces and a working knowledge of Bell's theorem. People jump from the first to the second, stall on Bell or Maudlin, and conclude the subject is beyond them. It is not; there is just a rung missing, and this order supplies it.
One thing to be clear about before you start: this is not a field with a settled answer that popularisers are withholding. Working physicists and philosophers of physics disagree, in print, about which interpretation is correct — and a good many think the question is badly posed. The books below are mostly written by advocates. Read at least two who disagree.
The history and the shape of the argument
Quantum tells the Bohr-Einstein debate as narrative history and is the most enjoyable way in. What is real? argues that the foundational questions were actively marginalised for decades by a physics culture that treated them as unprofessional; it is sympathetic to Everett and Bohm and does not hide it, which makes it useful rather than unreliable, but do not take it as a neutral survey.
Beyond Weird is the best short modern overview, and its particular virtue is demolishing the bad metaphors — the ones about particles being in two places at once — that make the subject harder than it is. The ghost in the atom is a set of interviews with the principals, Bell among them. It is short and old, and it remains the fastest way to hear the disagreement in the participants' own voices.
Enough machinery to have an opinion
Quantum Mechanics gives you the actual formalism at the lowest honest cost — Susskind's Theoretical Minimum approach, aimed at people who want the mathematics without a full degree. Quantum mechanics and experience is the bridge book: Albert derives the measurement problem carefully and slowly for readers coming from philosophy rather than physics, and almost everyone who works in this area has read it.
Speakable and unspeakable in quantum mechanics is Bell's collected papers, and there is no substitute. Bell wrote unusually well, and the theorem is his. Quantum non-locality and relativity is Maudlin's careful treatment of what Bell's result does and does not establish about compatibility with relativity — the single most commonly misstated point in the field. Quantum theory is Peres's textbook, written by a physicist who took foundations seriously while holding a strongly operational view; it is a useful counterweight to the realist books that follow.
One book per interpretation
Sneaking a Look at God's Cards presents dynamical collapse theories from a co-author of the GRW model — an interpretation where collapse is a real physical process with testable consequences. The Quantum Theory of Motion is the definitive technical treatment of de Broglie-Bohm pilot-wave theory: deterministic, explicitly nonlocal, and far more developed than its reputation suggests.
The Emergent Multiverse is the strongest modern statement of the Everett interpretation, including the hardest part, which is what probability could possibly mean if every outcome occurs. Decoherence and the quantum-to-classical transition covers decoherence — and it is worth saying plainly that decoherence is not itself an interpretation. It explains why we do not see superpositions at everyday scales; it does not by itself solve the measurement problem, though how much it contributes is disputed.
Work the path in order and you will finish able to state the strongest version of at least three positions. That is the realistic goal here — not picking a winner.
Follow the full ordered path here: How to Learn Quantum Foundations from Books, in Order.
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