What is the plot of Crime and Punishment?

I would argue that Crime and Punishment is a portrait of a madman. It is the story of Rodion Romanovich Raskolnikov, who murders an elderly pawnbroker and her sister in cold blood with no real motivation. He has been oblivious to the existence of Alyona Ivanovna until he happens to overhear a student in a tavern talking about how society would be better if Ivanovna was dead. This seemingly makes him decide to kill her.

The disturbing fact that Raskolnikov does not understand why he committed Alyona's murder becomes apparent gradually over the first few chapters. Lisaveta's murder was purely based on her being in the wrong place at the wrong time.

He is questioned by police, but is not suspected of having committed the crime. He later confesses to Sonia, a prostitute and family acquaintance, that his callous motive was simply to see if he would experience the normal levels of revulsion at such a crime. It becomes apparent that Raskolnikov is a psychopath and that to him, murder is about exerting the maximum amount of power possible over another person.

Raskolnikov is a greatly conflicted character, happy to commit murder on the one hand and on the other tortured by a dream about a horse being beaten to death. He eventually turns himself in with a plea of insanity and is sentenced to eight years of hard labor for his crime.