Hassan's actions demonstrate that he forgives amir's betrayal, although amir needs to spend practically the entire novel to learn about the nature of forgiveness and baba's treatment of hassan is his attempt at gaining public forgiveness for what he has not told everyone?

Hassan was Baba's son outside of marriage and Baba never told anyone about it.

Explanation:

In the novel, The Kite Runner, Baba is an influential and a very kind figure living in Kabul. However, he had an extramarital affair with Hassan's mother who was a servant at his house. Hassan is Baba's child but he never discloses it to public during his life but he showed him great affection especially during the time of Hassan's birthday. Hence, in a way, by acting kindly towards Hassan, Baba was trying to gain forgiveness for his act and for not giving Hassan his rightful status. Hassan and Amir, Baba's son with his wife, comes to know about this after Baba's death.