What are some central ideas of the Scarlet Letter?

One of the main ideas of The Scarlet Letter is that society often separates individuals from their true identity. As an adulteress in a Puritan society, Hester Prynne has had an artificial identity imposed upon her, an identity symbolized for all to see by the dreaded scarlet letter. As far as the moral guardians of the community are concerned, Hester's an adulteress: a sinful, fallen woman, and that's all that anyone really needs to know about her. The idea of her being a human being, deserving of respect and dignity, simply doesn't occur to them for a moment.
At the same time, the imposition of the scarlet letter for Hester's transgressions allows her to forge an identity of her own. Hester's a strong-willed, intelligent woman who simply will not accept that society has the right to determine who and what she really is. This defiant attitude explains Hester's surprising reaction to news that the town's elders are considering letting her remove the scarlet letter. We might think that she'd welcome the prospect of casting off this badge of public shame and humiliation. But Hester's thinking is that, if she is to remove the scarlet letter, it should be because she and she alone has made the free choice to do so, not because local worthies have graciously condescended to give their permission.