In studying QFT on curved spacetime I've found the $\ast$-algebra approach as one viable approach to the subject on the paper Quantum Fields in Curved Spacetime by Wald.
The $\ast$-algebra approach seems like one quite nice and general approach to both QM and QFT, but it is quite abstract, so that it seems hard on the beginning of the study of this approach to see how it is used in practice and how, in the end, it is just a generalization of usual QM.
The point is that in QM books, like Cohen's, after presenting the postulates, examples are given to emphasize what is the physical meaning of everything and how one works with it, like spin 1/2 systems, the harmonic oscillator and so forth.
Although Wald shows some examples, I believe more examples and more details would be nice to get started.
What I'm looking for here are references showing examples of the $\ast$-algebra approach in practice for both QM and QFT. In other words: some simple examples showing how to connect the abstractness of the approach with the underlying physics and the usual approaches.
Any kind of reference is good: books, papers, lecture notes, video lectures, etc.