The story is focussed around Amir's redemption after "watching Hassan get *****." He wasn't able to help his friend, and carried this guilt with him into adult life.
This is clearly a central theme in the novel, as the phrase "there is a way to be good again," spoken by Rahim Khan when asking Amir to save Sohrab, is present in the first chapter - the whole novel is set up around.
When Amir goes to save Sohrab and gets almost killed by Assef, he says that he "felt at peace," that he was "healed at last." It seems that, in fighting Assef as an adult, Amir has done what he could not when he was a child, and so has redeemed himself in this aspect.
However it is not until Amir takes Sohrab back to America that the true redemption takes place. Amir says that he will run a kite for Sohrab, using Hassan's words "for you, a thousand times over," and in doing this he takes Hassan's role. He becomes the honorable, pure one, and, in doing so, atones for his past sins.
Baba is also trying to redeem himself from his infidelity, by doing good things like "building and orphanage," and Soraya wants redemption for her past sins, which is possibly why she and Amir understand each other so well. Hosseini seems to be saying that it is always possible to redeem oneself, that everyone can make what's wrong, right.
Fathers and Sons
The story explores male relationships in the absence of women - both Amir and Hassan's mothers are not present.
Baba seems to dislike Amir, and Amir thinks this is because Sofia died in childbirth, and we also see that Baba thinks that "something is missing in [Amir]." Baba disapproves of Amir's storytelling, showing no interest until years later, when Amir finds his wife reading his stories to Baba, who says that "he put her up to it." It seems that Baba and Amir's relationship has been redeemed.
Also, when Amir goes to find Sohrab, he becomes the man the Baba always wanted him to be.
By contrast, Ali treats Hassan with love like a father, even though he not his real parent.
When Amir raises Sohrab at the end of the novel, it seems that, just as Ali had taken care of Baba's child, Amir can now return the favour and take care of Hassan's. Perhaps Hosseini is suggesting that being a father figure is more influential that being a biological parent.
Rahim Khan takes the role of a father figure for Amir, as his is supportive of Amir when Baba is not, saying that he has a "special talent."
The novel deals with what is means to be of Afghan heritage, and specifically an Afghan man.
One reason why Baba dislikes Amir is because he doesn't fit into what Baba thinks an Afghan man should be like, he says that " [he] wasn't like that at all, and neither were any of the kids he grew up with."
More than this, Amir fits in well with American culture, becoming a successful writer, whilst Baba finds it hard to adapt. It seems that Baba has a stronger connection to Afghanistan than Amir.
Amir stops talking in untranslated Afghani speech when he goes to America, possible showing how tenuous his link with the country was.
When Amir return to Afghanistan to save Sohrab, he says that he "feels like a tourist," and Farid replies that he as "always" been a tourist. Amir has never really fit in with Afghani culture, never really belonged there.
However, when Amir gains Farid's respect and they "become friends," is seems that he becomes more comfortable in Afghanistan; he has connected to his heritage.
Religion and Ethnicity
There are tensions between different religions and ethnicities throughout the novel.
Ali and Hassan are Hazaras, a different ethnicity than Amir and Baba, who are Pashtuns, and because of this they are bullied and ostracized.
Assef says it's okay to **** Hassan because he is "just a Hazara," showing how firmly to discrimination is entrenched in Afghani culture.
Ali and Hassan are also Shi'a Muslims, which leads to more discrimination being directed towards them. Even though they are arguably more devout Muslims than Amir or Baba, as Hassan "prayed the morning namaz with Ali" before Amir was even out of bed, they face persecution from the Taliban, who being Sunni Muslims, think that Shi'a Muslims follow the wrong branch of Islam.
It seems that Hosseini is commenting on the lack of respect for different peoples that is present in Afghanistan, and by having Hassan, the pure and innocent character, be part of an oppressed demographic shows how wrong this oppression is.