Short answers, pulled from the story.
Crime and Punishment was written by the Russian author Fyodor Dostoevsky. It was first published in the literary journal The Russian Messenger in twelve monthly installments during 1866, with the first part in the January 1866 issue and the last in December 1866, then later released in a single volume.
Crime and Punishment follows Rodion Raskolnikov, an impoverished former law student in Saint Petersburg who murders an old pawnbroker and her half-sister with an axe. The novel centers on his mental anguish, guilt, and moral dilemmas rather than the formal legal punishment for the crime.
Raskolnikov theorizes that certain extraordinary individuals have the right to step across moral and legal boundaries to achieve higher goals. He convinces himself he can kill a useless old moneylender to escape poverty and perform great deeds, an idea he lays out in his article On Crime.
Sonya, born Sofya Semyonovna Marmeladova, is the daughter of the drunkard Marmeladov and has been forced into prostitution to support her family. She becomes the first person to whom Raskolnikov confesses, reads him the story of the raising of Lazarus, and follows him to Siberia as a source of moral strength.
Dostoevsky wrote Crime and Punishment to counteract what he saw as the nefarious consequences of Russian nihilism, utilitarianism, and rationalism. He attacked a Russian blend of French utopian socialism and Benthamite utilitarianism, known as rational egoism, that had developed under thinkers such as Nikolai Chernyshevsky.
Raskolnikov confesses to the murders and is sentenced to only eight years of penal servitude in Siberia, partly because another man had already confessed. Sonya follows him there, and after some time in prison his moral regeneration begins under her loving influence.