Quantum Lectures on Quantum Mechanics by Weinberg

I'd not conclude that a textbook must be good, because it's written by a Nobel laureat, but in the case of Weinberg it's true. All his textbooks are just very well written with a clear exposition of the subject in a deductive way, which I myself always prefer compared to inductive expositions of a subject. Of course, also the history of science is important, and that's also covered by Weinberg in well written introductory chapters on the historical development of the theory.

Concerning the subjects covered the book is pretty standard for an advanced graduate course in non-relativistic quantum theory. All the important topics are covered, including a very clear foundation of the Hilbert-space formalism, which is used from the very beginning (after one chapter, where the hydrogen atom and the harmonic oscillator are treated in the wave-mechanical way).

In chapter 3 he gives a complete foundation of the quantum theoretical formalism in terms of the abstract Hilbert-space formulation, using symmetry arguments to establish the operator algebra of observables for non-relativistic quantum theory (i.e., using Galileo invariance as a starting point).

For me the most interesting part of chapter 3 is Sect. 3.7 on the interpretation of quantum theory, where after a very good summary about the various interpretations he finally comes to the conclusion that a complete satisfactory interpretation of the quantum theoretical formalism has not yet been achieved.

The rest of the book is simply a very good presentation of the standard material that any quantum mechanics course should cover, including the quantum mechanical description of angular momentum, time-independent and time-dependent perturbation theory, scattering theory (marvelous via the time-dependent wave-packet approach, which he has already used in his quantum theory of fields vol. 1 and which is, in my opinion, the only satisfactory derivation for the S-matrix anyway!).

The book closes with a concise exhibition of "non-relativistic QED", i.e., the quantized electromagnetic field coupled to "Schrödinger particles" and the final (unfortunately rather short) chapter about entanglement, discussing the interesting topics of EPR, the Bell inequalities, and quantum computing.

As usual with Weinberg's books, it's not written for beginners in the field but for the advanced graduate. These needs are better suited by Ballentines book, although also this one is rather tough for the beginner. Compared to Weinberg's book, in my opinion its main advantage is that also the mathematics of the rigged Hilbert space is developed to a certain extent.

For me, the best introductory text still is J.J. Sakurai, Modern Quantum Mechanics but Weinberg's is a must-reading for the more advanced scholar!