There are lots of themes you might want to draw out of this book. Each of these could be examined for an essay and traced throughout the novel. Here are a few to get you started...
The character of the father, Eugene Achike, clearly suggests the dangers of religious extremism. His attempts to control his family's life, even going so far as mapping out every moment of his children's day, shows exposes controlling nature of such fervent belief. His frequent bouts of violence also call into question his faith, exposing him as a hypocrite.
Another theme is the contrast between traditional beliefs and Western beliefs in non-Western societies. We can see this contrast played out in the contrast between Eugene Achike and his father, Papa-Nnukwu, who is a kind loving man who follows the indigenous beliefs of his culture.
The concept of silence and its consequences is likewise examined. The time that Kambili and her brother spend at the house of their father's sister is crucial, as this family, although Catholic, is open and the members are able to talk about issues. It is a nurturing time for Kambili and her brother. In contrast, it is arguably the silence imposed on the family by Eugene that leads to his eventual demise.
One of the themes of the book is the hypocrisy of traditional religion. Kambili's father, Eugene, is a devout Catholic, but he abuses his family. At the beginning of the book, he flings his missal across the room when Kambili's brother, Jaja, does not receive communion. Eugene also beats his wife senselessly until she is "slung over his shoulder like the jute sacks of rice his factory workers bought in bulk" (page 33). Eugene's religion is the traditional, westernized form of Catholicism, and his church features a blond Virgin Mary (though Kambili and her family live in Nigeria).
Another theme of the book is the goodness and veracity of the more authentic Catholicism that Kambili's aunt, Ifeoma, and her family practice. This form of religion is about helping others and being charitable--and not necessarily about following every traditional rule. For example, their priest, the young Father Amadi, does not follow orthodox rules (he wears shorts and doesn't spend time looking like a priest), but he is willing to help Kambili connect to Jesus. When he takes her to run in a stadium, he asks her to show her love for Jesus by running and feeling her own power. The brand of religion that Ifeoma follows allows her to help her father, who is a "heathen" because he is not Catholic, while Eugene's religion causes him to disavow his father. Adichie's book is about how orthodox religion is often hypocritical and unkind, while religion that comes from the heart and soul is true and good.