There are not that many science fiction detective stories out there--something about the contradiction between advanced technology and mystery, I suppose--but the ones that are (Asimov's Caves of Steel is one of my favorite guilty pleasures) can be rare finds. Bester's novel is a brisk tale while it is also a stylish tour de force and stuffed full of ideas.
The "hook" involves a murder in a society well-populated with telepaths. The murderer's identity is not in question--Bester sets that up quite early in the story--but the cat-and-mouse game between the murderer, Reich, and the telepathic policeman, Powell, is what drives the narrative. Add to that one of the most innovative methods of writing the complex interplay of telepathic communication I have ever seen, and some quite distinctive locales, and you have a fast-moving tale that is somewhere between E.E. Smith and Philip K. Dick. Yes, that's an unusual pair of writers, but you need to experience Bester to understand.
In fact, The Demolished Man shares a lot with Dick's later work, Ubik, but while the latter focuses on the metaphysical (and, to some degree, existential) dilemma the main character finds himself in, Bester's work is more concrete and down-to-earth. That's not to say it isn't a mind bender in its own way--but compared with Dick's almost endless house of mirrors in Ubik, Demolished Man seems almost prosaic in comparison.
Something else I admire greatlyin Bester's work is the timelessness. Science fiction is vulnerable to the passage of time like few other genres--technological advancements can render some plots quaint at best, obsolete at worst. But I can't imagine Bester's work ever becoming so. The only serious technological advancement in Demolished Man is a computer to which the police department must feed data until it determines the case worthy of prosecution, and although I'm sure what Bester had in mind would be hopelessly out of date now, it is not a major bump in the narrative.
The Demolished Man, and The Stars My Destination, are both well worth a read.