Rationalism as a trap
Raskolnikov builds an airtight logical case for murder and it destroys him. Dostoevsky shows that treating human beings as problems to be solved with theory, including yourself, cuts you off from the things that actually sustain a person.
Guilt as a physical force
Guilt in this novel is not just regret. It produces fever, compulsive behavior, and near-confessions. Raskolnikov's body betrays him before his mind does. Dostoevsky treats conscience as something you cannot reason away.
Suffering and redemption
Almost every character suffers. Sonya suffers and stays human. Raskolnikov suffers and becomes more isolated. The difference is whether suffering is accepted or resisted. Dostoevsky argues that accepting suffering is the only way through it.
The extraordinary man delusion
Raskolnikov's Napoleon theory is the engine of the plot. The novel systematically shows why it fails: violence cannot be contained, guilt cannot be suppressed, and the people Raskolnikov dismisses as ordinary turn out to be the ones who survive.
Faith against nihilism
Sonya's religious faith and Raskolnikov's cold rationalism are in direct opposition. Dostoevsky does not present faith as naive. He presents it as the only thing that keeps a person intact when everything else collapses.