Short answers, pulled from the story.
Fyodor Dostoevsky wrote Crime and Punishment during the summer of 1865 in Wiesbaden, Germany. The first part appeared in January 1866, and the final installment was published in December 1866.
Anna Snitkina, a stenographer who later became his wife, helped him complete the manuscript under extreme pressure. She typed out the text while he dictated it rapidly to meet deadlines for both Crime and Punishment and The Gambler.
Rodion Raskolnikov operates on a theory that certain crimes are justifiable if committed to remove obstacles facing extraordinary men. He attempts to kill Alyona Ivanovna, an elderly pawnbroker, to alleviate human misery through utilitarian-altruistic justification.
The streets of Saint Petersburg reek of unwashed bodies and rotting garbage during the summer of 1866 to serve as a physical manifestation of spiritual sickness and moral corruption. Crowded squares and shabby houses transform into metaphors for states of mind within Dostoevsky's narrative.
Fyodor Dostoevsky wrote letters to Mikhail Katkov revealing his immediate inspiration was countering doctrines of Russian nihilism. He believed such ideas limited man to products of physics, chemistry, and biology while negating spontaneous emotional responses.