What is Hannah's main goal in the The Devil's Arithmetic?

Hannah's immediate goal is survival. Once she realizes how dangerous her situation is, she needs to do whatever she can to avoid the terrible fate of so many Jews during the Holocaust. In turn, this means that the longer she can stay alive, the more she'll understand the predicament of her ancestors. This is her long-term goal.
Hannah had heard all the stories from her folks about the war and what it was like for the Jewish people, but she never truly understood their significance. As the story begins, she doesn't quite fathom why it is that her family insists on remembering the past. But once she steps—quite literally—into the past and takes on the identity of Chaya, she finally comprehends just why it is that historical memory takes on such great significance for her family and for the Jewish people as a whole.