The answer to your question can vary from one legal system to another, as each legal system may have different copyright laws, and an action that's considered a violation of copyrights in one country may not be considered as such in another.
That's being said, you should know that the "fair use doctrine" makes an exception to copyright law in many countries (including the U.S). According to the doctrine, copyright does not prohibit all copying or replication. In the U.S, the Copyright Act of 1976 allows some copying and distribution without permission of the copyright holder or having to pay to the copyright holder. The act doesn't clearly define what "fair use" is, but instead gives four non-exclusive factors to consider in a fair use analysis. Those factors are:
- the purpose and character of your use.
- the nature of the copyrighted work.
- what amount and proportion of the whole work was taken.
- the effect of the use upon the potential market for or value of the copyrighted work.
The doctrine, in some form or another, also exists in the UK and the Commonwealth countries, Canada, Australia and more. For example, I live in Israel, which was under British rule from 1917-1948. In that time, the English Copyright act of 1912 was in effect in Israel. When the Israel got its independence in 1948, the act was "imported" to Israeli law, and so. in a way, the British copyrights law is still in effect in Israel.
As far as I know, most countries regard writing about a copyrighted material as "fair use", when it's done as a criticism or as an academic paper. You should, however, remember that even so, your work will be tested by the four factors mentioned above. You can't, for instance, copy an entire book "en block", put quotation marks at the beginning and ending of the text, add the sentence "that's a very good book" and say "that's criticism, not a copyrights violation".
Hope it helps.