The narrator is by far the most interesting part of this book, as are most narrators who occupy a very different space than the typical reader does.
The book does not feature a spectacular plot (or even a terribly interesting one - the exegesis would run something like: dog is killed, narrator asks questions about dog's death, fights with father, runs away to mother, comes back home). What is interesting is viewing the characters through the perspective of a narrator who is incapable of deciphering the subtle visual and social cues that most of us would pick up on. In this way, he is a bit like Brittany, the narrator of Atonement, who misinterprets her sister's sexual engagement with a man as a victimization.
Here, the book employs first person narration by Christopher John Francis Boone, 15 years old, who doesn't understand much of the world around him. He observes everything, unselective in what he attends to, which overwhelms him sometimes. He is not good at reading emotions other than very basic ones and doesn't understand idioms. When frustrated or touched (he doesn't like to be touched), he screams, or groans, or does math problems (in a kind of trance). He's very good at math because it has a right answer all of the time whereas human relationships don't always have a right answer. He decides whether it will be a good or bad day depending on how many cars of a certain color he sees on the way to school (he likes red but hates yellow and brown).
He comes across his neighbor's dog Wellington stabbed with a garden fork and decides he will solve the mystery of who killed Wellington. He uses itineraries, maps, and logic to determine who might have killed the dog. He even goes door to door though it scares him to talk to strangers. Encouraged by his teacher, Siobhan, he decides to write it as a mystery, but his father finds the book and takes it away. When Christopher goes to look for it, he finds it in a box full of letters from his mother, and decides this is another mystery. Despite solving both mysteries, Christopher's relationship with his family has deteriorated by the end of the book and the final scene has Christopher discovering he got an A on the exam and determining he will write his A levels in physics and go to university when he is done school.