The novel is centrally concerned with Raskolnikov's crime of murder: the long buildup to it, the murder itself, and the aftermath. Raskolnikov kills Alonya—a miserly and horrible old woman—and Alonya's sister Lizaveta. These are his overt crimes. But the novel is concerned with far more than their deaths. There is the deeper crime of Raskolnikov's anger and alienation, which is what leads him to plan a murder. There is the moral crime of plotting a cold-blooded murder, and the additional moral crime of feeling no remorse. Readers are potentially complicit in the moral crime as well, because, to the extent they identify with Raskolnikov, they too will despise Alonya and perhaps, while feeling horror over the fact of the murder, not experience much horror over her death.
At the end of the novel, Raskolnikov fulfills his sentence in the work camp in Siberia in order to pay for his crimes. This is punishment for the act of murder. However, Raskolnikov, who does have a conscience, also suffers internal torment—self-inflicted punishment—over his inability to feel remorse. One could argue, too, that throughout the novel Raskolnikov torments (punishes) himself; the murders are simply the visible part of the submerged iceberg of a deeply tortured soul living in a deeply troubled society.
The title of Crime and Punishment fits the narrative and the themes because both the narrative and the themes are about crimes committed and punished or not punished. Let me clarify a little for you.Several characters commit crimes of varying sorts who are or are not punished for them.
An example of this is when Dounia shoots Svidrigailov for his attempted crimes against her. In so doing, she commits a crime. Yet she will not be punished for it because Svidrigailov will say nothing. Guilt from this incident and his other crimes weigh him down until he ends his life in shame and despair.
she raised the revolver ... and there was a pang of [desire] in his heart. He took a step forward and a shot rang out.
Other characters commit moral crimes that are not legal crimes. Two of these are Marmeladov and Luzhin. Each brings shame and suffering on the woman they desire, Marmeladov against Katerina Ivanovna a great more severely than Luzhin against Dounia, though. These characters may be "punished" by circumstances such as when Marmeladov dies so helplessly, yet this punishment leaves his victims in worse and more direful straits than before.
An example of this kind of crime is Sonia. She is forced as a result of Marmeladov's moral crimes to accept being registered for a "yellow ticket" that allows her to commit the crime of prostitution without fear of punishment.
Sonia ran to restrain Katerina Ivanovna, but when Amalia Ivanovna shouted something about "the yellow ticket,"
The title most significantly applies to Raskolnikov, of course since he is the one who commits the heinous crime against Alyona Ivanovna, "the old lady." And it is Raskolnikov whom the police pursue and catch....
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It is Raskolnikov who is punished in a Siberian prison camp for his crime.
"Will you come and see me in prison when I am there? [...] Sonia, you'd better not come and see me when I am in prison." (Raskolnikov to Sonia)
Now you can see that the title is perfectly suited to the narrative because in it Dostoevsky explores many forms and degrees of crimes committed against other persons and punishment meted or escaped for the crimes. We mentioned a few instances, but there are others, like Luzhin's attempted crime against Sonia where he wrongly accuses her of crime.
"if it had suited his plans, [Luzhin] would have sent you to prison if it had not been for Lebeziatnikov and me. Ah?" (Raskolnikov to Sonia)
How does the title Crime and Punishment fit the book?
The title forces the reader first to think about what a crime actually is. Most would picture literal crimes such as Raskolnikov's murder of the pawnbroker. However, Dostoevsky forces his readers to consider other crimes that are not always visible.
In regards to the "punishment" in the title; again, the reader must interpret beyond the literal punishments such as one serving time in prison. Raskolnikov's true punishment is his inner conflict, the guilt which leads to physical and even mental illness because of its consumption of Raskolnikov's soul.
Moreover, the reader must also consider, in general, what makes a punishment fit the crime? How much time is enough for one to be punished for a crime?