Grief
Violet and Finch both deal with grief. Violet has been severely affected by the death of her older sister Eleanor and does not cope well, becoming a shell of the person she once was, alienating herself and trying to stay under the radar. Her parents do not deal with Eleanor's death out in the open, which frustrates Violet and causes her to further retreat from the outside world. Finch, in his own way is grieving: he grieves his lost father, who didn't die but did abandon them, and did hurt them. Furthermore, Finch seems to be someone who has always had grief in him—the story of the cardinal, which so affected him, seems to have cemented this deep well of grief that he cannot escape, which is tied up with his depression. Ultimately, Finch gives Violet the gift of carrying her through her grief, allowing her to experience all the sadness and anger and confusion she needs, while also nudging her forward, helping her see that she still has a life to live.
Guilt
Guilt, particularly survivor's guilt, is explored throughout the novel. Violet survived a car accident that killed her sister, and is continually reckoning with what that means. Why is she alive but not Eleanor? Will people walk on eggshells around her forever? How does she live her own life without forgetting Eleanor? She dislikes the way her parents, teachers, and counselor talk about being a survivor; only when she meets Finch does she start to understand some of the complex emotions she's feeling. When he dies, she again experiences this guilt, feeling like she could have done more, she could have saved him. In a conversation with Finch's counselor, Mr. Embry, he tells her that he, too, feels some guilt, but that ultimately his survival wasn't up to either of them. As if anticipating that Violet would feel guilty for his death, Finch leaves a letter for her with song lyrics, showing that she was the best thing that happened to him, that she made him so happy. Only then, reading his words, does she let go of the guilt.
Love
The romantic relationship between Violet and Finch is central to the plot of the story. Finch realizes early on in their friendship that he has feelings for Violet, and fairly soon she begins to develop feelings for Finch as well. As their relationship grows and becomes more intense, Violet begins to heal and open up to Finch. In Finch’s case, Violet is one of the main reasons he wants to stay "awake." It's more than just lust or attraction; the novel shows how deep, real love is a singular life-giving force. Even after Finch is gone, Violet's love for him—and his love for her—will ensure that she will live a beautiful life.
Suicide
The novel opens with two characters contemplating suicide, so the plot clearly establishes that is a main concern of the book. While this is more of a one-off moment of desperation for Violet, Finch has a chronic history of suicidal thoughts and behavior. In his journal each day, Finch records facts and anecdotes about different methods of suicide. He is ranked number one in the school gossip site's list of most suicidal students, and treated as a social outcast. He doesn't want to die, but sometimes, when he is feeling really bad, his brain convinces him that the nothingness of death would be a relief, and he finds that intoxicating. He fixates on Virginia Woolf, who died by suicide, drowning herself in a river, which foreshadows his own death. In the novel, he attempts suicide once before he dies by taking half a bottle of sleeping pills, but he makes it to the hospital in time. He attends a suicide support group after that, where he learns that Amanda Monk has also attempted to kill herself. In the end, Finch does die by suicide, and it's difficult for Violet to understand why he did it.
Mental illness
Finch experiences what he calls "black moods," which, technically speaking, are bouts of severe depression. In his family, mental illness is stigmatized: his mother only believes in physical illness, and would tell him to take a painkiller if he said he was feeling bad. At school, the stigma is even more pointed. Everyone calls him a freak, thinks he's crazy because he has a tendency to lash out in anger, to be emotionally volatile, to miss school for long periods of time. Finch is ostracized because of his mental illness, made the butt of everyone's jokes. In reality, many people are struggling in some capacity with their mental health, but because they all fear being ostracized, they double down on bullying Finch; if he's the focal point, they will be protected. We can see how deeply this stigma has affected Finch when Mr. Embry suggests he might have bipolar disorder. Rather than feel relieved to be able to name the things he's feeling, and understand that it's not him, it's an illness, Finch becomes enraged at the label, believing that a diagnosis only reduces a person to something that can be explained away. While Finch's worries are completely valid, the conversation is an interesting one: if Finch had accepted his diagnosis, and told Violet and his family about it, and sought targeted treatment for it, he might have been able to feel better.
Family & family trauma
As the main characters are still in high school, their relationships to their families play a significant role in their lives. While Violet's parents repress their sadness about Eleanor and are occasionally overly cautious, they are ultimately caring and loving people who want what's best for their daughter. At first, Violet feels the need to hide things from them because she can't bear to pile onto their sadness, but eventually she opens up to them again, and they do what they can to help her. Even when Violet admits that she'd been seeing Finch against their wishes, they put their anger aside to do the right thing and try to help him. By the end of the novel, they have begun talking about Eleanor again, and we have the sense that the Markey family is going to be okay because they have each other. Finch's family, meanwhile, is entirely dysfunctional. His father is physically and emotionally abusive, and abandoned their family to start a new one. His mother, in her grief, has totally shut down and grown neglectful. She never knows where Finch is, doesn't even know when he's been expelled from school. His sister Kate takes on a quasi-parental role, but she is only nineteen; his younger sister, Decca, struggles with her absent parents. When Finch is missing, Violet is far more concerned than his own parents, and this drives home one of the great tragedies of the book: no matter how much love he gets from Violet, it will never compensate for the love he isn't given by his parents.
Wandering
Wandering is a major theme of the novel, and, in terms of plot, is what kicks off the story between Finch and Violet. Their geography project is what moves them out of the sphere of school and into the outside world, and is a steady thread throughout the novel. Even in the end, after Finch's death, Violet must finish the project; in doing so, she discovers Finch's last messages for her, and finally reaches a point of forgiveness. Finch is obsessed with the notion of wandering—it seems to relate to his desire for a Great Manifesto, and his need to always be on the move, making forward progress. For Finch, there is meaning in wandering, meaning in discovery; to look for new things allows him to escape from what weighs on him. He creates a dichotomy between being lost and wandering (being lost is bad, and dangerous, while wandering is good, and meaningful), which we see in the scene with the crane. Together, Finch and Violet share all the places they'd like to wander, and after he dies, Violet continues to imagine where she'll go. For them, wandering signifies finding meaning, finding beauty, and continuing on.