I'd just like to add a little more about how the father and son change.

Elie begins as an educated young man who, by the end of the story, is wise and old from the experiences he and his father have had to endure. Being a Hasidic Jew, his faith was the center of his life until the Holocaust. Although he never totally loses his faith, he questions a God who would allow such horrible acts to happen to human beings. He is angry that God is not answering the prayers of the victims of the death camps. He stops believing in a merciful God, and instead, places the survival of his father and himself as the one thing he must believe in. At one point, Elie begins to resent his father and even considers taking his father's food ration. This is an understandable thought of a young boy trying to survive unthinkable circumstances. What is important is that he doesn't take his father's food, but it underscores that all Elie can believe in is to keep himself and his father alive. At the end, he sees his mirrored corpse and realizes he must believe in "healing humanity". The atrocities of the Holocaust will stay with him forever. His goal is to live his life telling people that the Holocaust was against human beings as a whole, not just Jews and the other groups singled out by Hitler.

Elie's father begins the story as a man who is greatly respected by everyone; he has lived his life up to that point showing more concern for others than for his own family. After going to the death camps, his only concern becomes keeping his son alive.

Here's an excerpt from the enotes character section, for more info follow the link below:
Eliezer had once believed profoundly and had lamented before God but he could no longer do so. He "felt very strong" in this realization for he "had ceased to be anything but ashes, yet I felt myself to be stronger than the Almighty." Eliezer is henceforth, except for a few moments of doubt, determined to live as a man (a being made of dust) and survive—"something within me revolted against death." Eliezer may no longer believe in the merciful and just God but he believes even less in giving into death by concentration camp madness. he is bent solely on survival and only his stomach takes note of time. Still he survives but merely as a corpse in a mirrored gaze just waking up from the long night.
Eliezer's father, Chlomo, is a "cultured, rather unsentimental man ... more concerned with others than with his own family." He is held in great esteem by the community and symbolizes Abraham. As Abraham, however, he refuses to sacrifice his son. He lives, while in the death camps, to try and keep his son alive. Eliezer, as a representation of Isaac, also safeguards his father. This relationship is the most important of the story. The bitterest moment comes when Clomo believes himself selected and gives Eliezer his inheritance—a knife and spoon.