In 2004 I wrote a survey on hardness of approximation as a book chapter for a book on approximation algorithm. I have just prepared a revised version for a new edition of the book.

While it would have been preferable to rethink the organization and start from scratch, because of time constraints I was only able to add sections on integrality gaps and on unique games, and to add references to more recent work (e.g. the combinatorial proof of the PCP theorem, the new 2-query PCPs, the tight results on minimizing congestion in directed networks, and so on).

If your (or your friend’s) important results are not cited, do let me know. The deadline to submit the chapter has long passed, but the threats from the editor haven’t yet escalated to the point where I feel that I have to submit it or else.