There are two questions, namely what you can do legally and what the community would consider acceptable.
Legally, distributing such a summary is probably a copyright violation if you borrow too much from the original; in the U.S., it would be considered a derivative work (the legal definition includes "abridgment" and "condensation" as forms of derivative work). In that case, it would be illegal to distribute it without permission from the copyright holder. On the other hand, you are not likely to get in trouble unless you offend the author or publisher. The easiest way to offend the publisher would be if they view your summary as competition that might decrease sales of the book, but they might take a strict approach to copyright enforcement in any case (it depends on the publisher, and I would guess that a nonprofit publisher might be more understanding than a big commercial publisher). In practice, the worst case scenario is probably being forced to take down any copies you had posted online. You could be sued, but that seems unlikely to me.
The research community is likely to take a less strict approach than the law. If you distribute the summary privately (e.g., just to friends or students), then nobody is likely to find out or care. If you post it online, then it's more likely to attract attention, but it won't necessarily be negative attention. That depends on how you've written it.
You should keep several things in mind to avoid causing offense:
You should be absolutely clear about what you have done: what's a direct quote, what's a mildly reworded version of the author's words, what's a summary in your own words. You need to be careful about distinguishing your own interpretaton from the author's, and you can run into trouble in two directions, either by seeming to take credit for observations that are explained in the book, or by seeming to attribute your own ideas or organization to the author. This is a difficult balancing act, which is easy to mess up. Even if you are very careful, the author may still feel that you are distorting the emphasis on different topics, for example.
You should be very careful about correctness. I would be unhappy if someone circulated a summary of a book of mine that had mistakes in it.
I would not recommend asking the author for permission, since that would put the author in an awkward position (of having to either endorse or object to your summary). If the author discovers your summary and complains, then I feel professional courtesy requires you to make changes or take it down.
Personally, I would probably not post it online, but opinions could differ.