It is difficult to summarize an entire book only in a single book review, when I want to have the ability of navigating through it later in my life, as a way of revising/going back for the data I took into me. I am thinking to write review on every chapter of a book or certain chapters together, depending on the density of content. Is it allowed to do that? Would there be any problem considering legal rules?
Generally speaking, quotation for purposes of criticism is an allowed use under copyright law. That does not necessarily mean all quotation in a review is permitted usage, though. You should make sure it is genuinely done for the sake of critique. But IANAL and there are plenty of better resources on permitted use available.