Wolfgang Pauli proposed the neutrino in 1930 in a letter that apologised for inventing a particle he believed nobody would ever detect. It took twenty-six years to find one, another four decades to prove it had mass, and that mass remains the only laboratory evidence that the Standard Model is incomplete. Almost every good story in this subject is a story about a null result that turned out to be real.
That history is also why the reading order matters. The popular books were written at different points in a long sequence of reversals, and the technical books run from an undergraduate particle text to a seven-hundred-page reference that assumes quantum field theory throughout.
The story, twice
Start with Neutrino by Frank Close. It is short, precisely written, and better than the alternatives on both the physics and on Bruno Pontecorvo, who proposed oscillation and then defected to the Soviet Union. Follow it with The Neutrino Hunters by Ray Jayawardhana, the better narrative of the search itself, from Reines and Cowan at a reactor through detectors buried under mountains and in Antarctic ice. Ghost Particle by Alan Chodos covers similar ground more recently and can be read instead of Jayawardhana rather than as well as, since the overlap is substantial.
The physics around it
Particle Physics: A Very Short Introduction, also by Close, supplies the rest of the Standard Model in about a hundred and fifty pages, which is what makes the neutrino's oddity visible in the first place. Deep down things by Bruce Schumm goes considerably further than most popular accounts, taking gauge symmetry seriously with very little mathematics, and it is the best possible preparation for a real textbook.
The elusive neutrino by Nickolas Solomey is an illustrated volume and a useful period piece, but note that it predates the 1998 atmospheric oscillation result, so its account of the open questions is now itself history.
The textbooks
Introduction to elementary particles by David Griffiths is the standard undergraduate entry, assuming quantum mechanics and special relativity and teaching Feynman calculus through worked examples. Modern Particle physics by Mark Thomson is the more current book at roughly the same level, with notably better neutrino chapters that treat oscillation properly rather than by analogy.
Then the specialist monographs. Neutrino Physics by Kai Zuber is the broad graduate survey of the whole field, experiment included, and is the right first specialist book. Fundamentals of neutrino physics and astrophysics by Carlo Giunti is the heavyweight reference, long and demanding, with field theory assumed on nearly every page. The physics of massive neutrinos by Boris Kayser is a much shorter and older monograph focused on mass and mixing, and it is a good way to test whether you are ready for Giunti.
Neutrinos as astronomy
Neutrino Astrophysics by John Bahcall is the classic, written while the solar neutrino problem was still unsolved and his own solar model was under suspicion; reading it knowing how the story ends is unusually instructive. Solar neutrinos collects source material on that same problem. Neutrino Cosmology by Julien Lesgourgues closes the path with the role neutrinos play in structure formation and what cosmological data can say about their masses, and it assumes a cosmology background.
What the detectors can and cannot see
Keep the limits in view while you read. Neutrino detectors register a vanishingly small fraction of what passes through them, and their angular resolution is poor next to any optical instrument, so pointing back to a source is hard and has succeeded only a handful of times: the Sun, the 1987 supernova in the Large Magellanic Cloud, and a small number of candidate high-energy sources. Oscillation experiments measure differences between squared masses rather than the masses themselves, so the absolute mass scale and the ordering of the three states remain open, as does whether the neutrino is its own antiparticle.
Follow the full path and these discoveries read as a chain of arguments rather than a list of dates.
Follow the full ordered path here: Best Books on Neutrinos and Neutrino Astronomy.
