Has there been a project to apply machine learning to generation of indices for books? Generating an index for a textbook is a tedious task. Can one automate it with machine learning? Are there any references to previous attempts in the literature to do this?
 A: To add on to the answer by @denis-tarasov, I would refer you to this amazing article by the Guardian.
Take a look at this passage:

One of the things that’s commonly imagined is that indexing is, in the age of Google, something that can be outsourced to a computer algorithm. Dead wrong. A concordance – essentially, an alphabetical list of all the words in a book with page references – can be done by a computer. But an index, to be useful, needs to be done by a human. In a book about the Middle East, say, an entry that said: “Syria 2, 3, 5, 6, 7, 10, 23, 25, 26, 27 … ” would be no use at all.

Indeed, the main argument is that keyword/keyphrase extraction cannot replace the human element of wittiness, critical thinking, and engagement with the reader of a book.
A: I think this problem is very similar to keywords/keyphrases extraction problem. Keywords extraction is well studied task (see for example this paper for review). Possible approaches include  heuristics, supervised machine learning (with a number of special feautures like TD/IDF, position in the sentence and other) and  language models. Powerful keywords/keyphrases extraction tools exist, thus one can try them first, and see if they do job well.   
