In The Hunger Games how does Katniss develop from the beginning to the end of the book?
Considering The Hunger Games, the first book of the trilogy, alone, it is in fact difficult to see Katniss's development. However, she is not the same person at the end of the Mockingjay, and in retrospect, the reader can see that the changes began during the events described in the first book.
As mentioned in the previous answers, Katniss is not afraid to break rules and she is single-mindedly focused on her and her family's survival. Even her volunteering to take Prim's place in the Games might have been more due to practicality, rather than sentimentality—Katniss is older and more likely to survive. This is not surprising given that survival has always been a struggle, and there was simply no time, or strength, for anything else.
This starts to change during the Games, when the struggle is not simply to survive, but to survive without becoming a murderer. At first, when Peeta mentions to Katniss the night before the Games that he does not want the Games to change him—to make him a savage—she is annoyed. But as she meets other tributes, particularly Rue, she begins to understand and relate to what he meant. So, her world is no longer black and white. She develops connections to people outside of her family. She realizes that Peeta has known her for years—she has been "a subject of dinner conversations" in his family—and her actions had left imprint on the residents of District 12, something she never considered before.
As the series progress, Katniss becomes less and less judgmental and narrow-minded. She becomes much more forgiving of other people's faults, such as Haymitch's drinking and the silliness of her "prep team." She begins to try to forgive her mother, whom she resented since she was too depressed to care for her children after the death of Katniss's father. While in District 13, she even develops friendship with Johanna Mason, a tribute from District 7, who she originally despised. In other words, as the story evolves, Katniss becomes compassionate and perceptive. This perception might have been what enabled her to see Alma Coin's impeding takeover of Panem for what it was, and change the course of history single-handedly by killing her.
I must agree with deem1510 in that Katniss does not sprint across the finish line but limps through it. At the end of the trilogy, having lived through the violence and the constant danger of the Games and the war, she is suffering from post-traumatic stress. But she still finds the courage to face each day, to help rebuild the District 12, and to raise children, despite her great reluctance to take this risk.
If I am being honest, I do not believe that Katniss does change and develop over the course of the novel. She hates the Capitol and its power from the beginning of the novel to the end. She is rebellious throughout the entire novel. She refuses to play by the rules. We see that at the beginning when she is out illegally hunting, and we see it at the end when she forces the Gamemakers to allow two winners. She is brave throughout the entire novel, and she is more than capable of holding her own. She constantly shows an ability to adapt and think on her feet, and for the most part, she cares more for her own survival than anybody else's survival. It is something that Gale points out in the third book:
"Oh, that I do know." I can just catch Gale's last words through the layer of fur. "Katniss will pick whoever she thinks she can't survive without."
While Katniss is focused on her own survival, there are a few exceptions when she does consider the welfare of someone other than herself. The best indication is the Reaping. Prim's name gets chosen, and Katniss decides to offer herself as tribute instead. During the actual Hunger Games, Katniss is offering some protection to Peeta and Rue, but readers are often left suspecting her motivations. Is she really protecting them or just using them as tools for her own survival and manipulation of sponsors?
If I had to pick some kind of specific way that Katniss shows some kind of actual development, I would pick the part of the novel right before she and Peeta are going to commit suicide. It is at this moment that Katniss realizes that she can actually beat the Gamemakers at their own game. She realizes that she, as an individual, can fight and win against the Capitol's oppression. Up until this moment, Katniss does not believe any of her actions will make a difference in the overall state of the world:
We both know they have to have a victor.
Yes, they have to have a victor. Without a victor, the whole thing would blow up in the Gamemakers’ faces. They’d have failed the Capitol. Might possibly even be executed, slowly and painfully while the cameras broadcast it to every screen in the country.
If Peeta and I were both to die, or they thought we were…
My fingers fumble with the pouch on my belt, freeing it. Peeta sees it and his hand clamps on my wrist. “No, I won’t let you.”
“Trust me,” I whisper. He holds my gaze for a long moment then lets me go.
Specifically in the novel The Hunger Games, and not including the other two books in the series, Katniss Everdeen's character changes through the influence of her experiences in the Capitol and in the arena of the Hunger Games. From the very beginning of the novel, she reveals herself as being a character of great heart and compassion for the ones she loves, like when she volunteers to take Prim's place at the reaping.
As the novel progresses, she becomes even more focused on surviving for Prim's sake, but the challenges of the Games force her choose between survival and her own humanity. From Rue's death to the horror of the muttations, Katniss has begun to despise the Capitol, but also has the strength to challenge their regime. By the end of the novel, the reader sees a Katniss who has matured even more and has finally realized the true dangerous nature of the Capitol.
She turned from someone who was poor to someone that ended up winning the hunger games.
Katniss starts out as a strong independent woman and by the end of the series she is depending on Peeta. She looses her independence and becomes weak to both Peeta and Gale.
Through the whole series she kind of.. undevelopes. She's not a Buffy, she's not a Bella. She limps across the finish line when we're used to seing main characters sprinting. She lives the rest of her life with just Peeta and her kids, because the real Katniss isnt the one that stories will be told about. Someone that finds life almost unbearable? No, she has no place in their stories. Which is really the only reason I think she "undevelopes". Ofcourse you could argue that through dialogue and plot Susanne Collins developed the character traits and personality of Katniss Everdeen. You could say she realizes a lot of things about life, and because of her misfortune she's grown. Either way, I guess