Familial Love
One theme of the book is the love between family members. Luke's parents, especially his mother, loved him so much that they defied the law of the land in order to give birth to him and raise him. Even Luke's brothers, who constantly tease him, keep the secret of their brother's existence.
Another example of familial love occurs between Jen and her step-father. Even though he is a member of the Government and cannot publicly acknowledge his third child, it is because of his love for Jen that her father obtains a fake ID for Luke, because he also cared about Jen. Throughout the book, the author suggests that familial love can help people resist a corrupt government.
Freedom and Safety
Many characters in the book have to make the choice between freedom and safety. Luke's family emphasizes safety over freedom, and, in a series of increasingly restrictive regulations, they forbid Luke to go outside, sit at the dinner table, and spend time with other family members. This increasing helplessness pushes Luke to take the enormous risk of making contact with the Sports family's child.
Jen, on the other hand, emphasizes freedom over risk. She does things that even Luke thinks are dangerous, such as pressing her face to the window or sneaking out to go shopping with her mother. She refuses the more common path of obtaining fake identification, and she organizes a group of Shadow Children to stage a protest in front of the President's house, saying that if they came out into the open there would be too many of them to kill.
Eventually, Jen's emphasis on freedom over safety results in her death at the hands of the Government after she stages a protest. However, her courage also inspires Luke to take the more calculated risk of obtaining fake identification and starting a new life as the adopted child of a Baron family.
Governmental Power
In the world of the novel, the Government controls where its citizens can live, what foods they can eat, and even how many children its citizens can have. The term for this kind of political rule is totalitarianism: the Government controls every aspect of its citizens' lives.
Luke's family believes that the government possesses the power to watch citizens through televisions and computers, and they are careful to hide Luke's existence even from extended family members and neighbors. However, when Luke meets Jen, she introduces him to the fact that the massive governmental apparatus is actually quite clunky and inept. She is able to connect with other Shadow Children through the internet, and they even go shopping with her mother.
However, the Government still possesses the power to kill Jen and her fellow protesting Shadow Children. It is also able to track Luke's location at Jen's house when he sends a message to the now-defunct chatroom for Shadow Children, and it is only the intervention of Jen's father that is able to save him. Overall, the Government's inconsistency in enforcing rules and establishing its power makes it more frightening, since it's not clear which actions will result in detection and death.
Truth and Ignorance
In a world defined by a corrupt Government in which some children must hide their existence entirely, the truth is a difficult thing to pin down. Jen presents Luke with a number of hefty books about the population problem that suggest it is more of an issue about the distribution of resources rather than overpopulation, but Jen's father later suggests that these sources are just as biased as the Governmental propaganda. At the end of the book, even a reader sympathetic to the plight of the Shadow Children struggles to know if repealing the Population Law would be the right course of action.
Deception
Nearly all of the characters engage in deception. Luke's parents deceive the government about the number of children they have, Luke deceives his parents about his visits to Jen's house, Jen deceives her parents about her online activities, and Jen's father deceives by using his position in the Government as a method to help Shadow Children. Eventually, Luke must embark upon a life of deception when he takes on a new identity as a Baron and heads away to a boarding school.
Power
One of the central questions of the book is this: who has power? Part of the reason that the Government limits the population is that it seeks to impose its power over citizens, but, as Jen insists, the citizens actually outnumber the Government and can rise up against it. Government theoretically has the power to limit population, but as we see in the book, this rule is often broken.
Luke's parents seriously restrict his movement and activities, exercising their power over him, but Jen calls into question why he should give them this power over them since they would be the ones who would get in trouble with the law for harboring a Shadow Child. Jen also uses her status as a Shadow Child to manipulate her parents into giving her various freedoms.
Social Status
The author gives many clues to suggest that Luke's family does not have much money. Their meals are simple, their clothing and furniture are patched and worn, they have few pieces of expensive technology, and they worry about how to make ends meet when the Government forbids them from raising hogs. In contrast, Jen's family lives in a large house in a new neighborhood, and they spend a large amount of money on expensive sports equipment. However, the marginal status of Luke's family allows them certain privileges because they're able to evade Government detection - for example, they eat meat, which is a rare commodity for the general population.
As the friendship between Jen and Luke grows, they sometimes struggle to connect in light of their vastly different social status. Perhaps because of her privileged upbringing, Jen insists on staging a rally in which Shadow Children can demand recognition from the Government, but Luke insists that he doesn't have the power to change history. Eventually, when Luke takes on the identity - and therefore the social status - of a Baron child, he plans to use this new privilege to create a world in which Jen's dream of freeing the Shadow Children can come true.