Would this be illegal?

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Hm...not sure if it would be legal. If it includes material from the game (screenshots or the like) that could be kind of a grey area. Reviews, Let's Plays or the like are "fair use", but a guide book might be taking things too far, since you're indirectly selling material that belongs to Frictional Games. I'm by no means an expert on the subject though, so I could be completely wrong there...

In any case, I doubt people will pay money for it. There is just too much free guide/ wiki material available and quite frankly, Amnesia is not really the kind of game you'd need a guide for in the first place. I mean, its practically impossible to fail at it, since nothing can really kill you and the puzzles are pretty easy too. Overcoming your fear is the only difficult thing about Amnesia and no guide can help you with that