The book, by James M. Cain, like the movie, is close to perfection. If I were teaching a course on adapting novels into screenplays, I would use this book and the Billy Wilder film. There are a lot of similarities, especially the voice of Walter Huff, the murderous insurance salesman (Walter Neff in the film), but there are many differences as well. Co-writers Wilder and Raymond Chandler came up with a much more cinematic ending for the story, but there best addition was to beef up the friendship between Walter Neff and Keyes, the claims investigator played by Edward G. Robinson.
Where the book is better is the characterization of Phyllis Nirdlinger (Dietrichson in the film), especially toward the end, when her crazed psychotic side comes out. It wouldn't have fit in the original film version, but it was superbly creepy in the book.
The copy I have, and the copy I read, is the Signet books version pictured above. It's from the 1950s, after the film came out, and what's funny about the cover art is that it is a scene that is taken from the movie that never happens in the book. Maybe the cover artist was like a kid who has to read The Great Gatsby for class and sees the movie instead. It's not a tie-in book, either, and if you look at the picture closely, it's clear that Keyes looks like a slimmer version of Edward G. Robinson, Walter looks like a red-headed version of Fred MacMurray, and Phyllis doesn't look remotely like Barbara Stanwyck.