My rating of Neonomicon is arguably unfair; I give it only one star foremost because it was wanting of a critical component: a massive TRIGGER WARNING!!! TL;DR: it needs one, and the scenes responsible for this requirement are not written well. 
 I am fond of H. P. Lovecraft, and I enjoyed the first part of the story (which is also collected separately in The Courtyard); it reminded me of the aspects of Lovecraft's writing that I enjoyed. As well, it did not shy away from noting the aspects that should neither be glorified nor forgotten: that Lovecraft was hella-bigotted. If you're comfortable with mild gore--or rather, I might better describe it as tasteful gore--then it could be fun. 
 The second part, 'Neonomicon'--which expands on the first story--didn't grab as much of my attention, but I was soon interested. It branched out from Lovecraft, into other contemporaries, and it was conservatively meta. It had Dr. Manhattan-esq philosophizing on the nature of reality--particularly time--and I wonder how much was Alan's philosophy, and how much a Lovecraft fan's headcanon. 
 But! the trigger warning! I will not detail the the occurrence. But as I began reading (intending to go sleep after finishing that chapter) I realized I now had to read the whole story, in hopes of feeling comfortable. It worsened, but not how one might expect! It was a later scene, involving the characters, which was far too glib--this is what most put me ill-at-ease! I have resigned to not consider, tonight, why this subsequent scene took such a tone--or if this tone was intended. 
 What I am now considering is how many a reader might enter into this story without knowing what Alan and Jacen depict for ten damned pages, overall!!! 
 There is more to be said about both stories, and their treatment of race and gender, but these contemplations have been eclipsed, for the moment. I am not triggered by what was depicted but many, many others are! And many who aren't would still likely prefer to know. 
 And, a thought on Trigger Warnings: I support them because it is not a matter of readers being underexposed and needing to toughen up (or whatever the bull**** people argue is--and it isn't your place, imaginary person, to tell someone to toughen up by reading a book!) 
 Trigger Warnings are for people who have been exposed to much more than others might fathom. Trigger Warnings take away nothing from the story and they can make a book more accessible. I still probably would have read Neonomicon, had it a trigger warning, because Trigger Warnings are not reviews. 
 if you are attempting to prove to someone the need for Trigger Warnings, I recommend you check Alan Moore's Neonomicon out of your library and suggest that they read it. Then, before returning it, make one of your own and stick it on the cover.