The main theme of Crime and Punishment is what happens to a man who grants himself, for the sake of an idea, the right to kill. The book does not ask whether Raskolnikov will be caught, but what the crime does to the one who commits it and what reason, alone, can or cannot sustain.
The police have no proof. The siege is carried out by his own conscience, by Porfiry, who understands him before any evidence, and by Sonia. Right after the crime, the narrator speaks of "a dark feeling of tormenting and endless solitude," and the body gives away what the head denies: he examines his clothes for blood, hides the theft without looking in the purse, and faints at the police station. The theory falls before the punishment.
Around this axis turn related themes. Reason: Razumikhin says that "a living soul will not submit to mechanics," and Raskolnikov starts from the arithmetic of one death against a hundred lives. Pride: in the Epilogue, he falls ill "from wounded pride." Guilt, compassion, and suffering: Porfiry says that "in suffering there is an idea." Money and poverty: Razumikhin, with the same poverty and the same interrupted studies, does not reach the same conclusion. And redemption, offered by Sonia as a rite and by Porfiry as a path.
The ending does not resolve the theory; it suspends it: in place of dialectics, the narrator says, "came life." Readers see in this the religious answer that a life gives to a thesis without needing to argue; others see the book's refusal to demonstrate the change it announces. Both readings coexist.