In academia we collectively evaluate the validity, quality and significance of shorter publications - papers - with a complex system of conferences and journals. With all its flaws, you can get a typically-not-so-bad idea about those aspects of a published paper by looking at things like venue and citations.
But that's not the case with books. I don't have any experience publishing books, but obviously it's not the same process as for papers.
Now, suppose I've entered a field which I've studied through papers; and I now want to either teach from a book, offer it to someone for some concentrated self-study, or cite from it. Also suppose I have some specific books I'm considering. How would I obtain some sort of evaluation or review of them, overall or by specific criteria such as correctness of proofs, rigor, clarity, narrative flow, being up-to-date etc.?
Note: Of course you can evaluate a book pretty well by reading it, but the idea is to choose what to get and read.