How does Harry Potter evolve throughout Harry Potter and the Sorcerer's Stone?

Harry Potter not only grows in confidence, but with that confidence, he also learns to value his voice and ideas. At the start of the novel, Harry generally expresses himself in short phrases; he realizes that his ideas are unwanted by his Aunt Petunia, Uncle Vernon, and cousin, Dudley. This is seen at the start of chapter two when Aunt Petunia knocks repeatedly on Harry's closet door. She demands,"Get up! Now! . . . Are you up yet" to which, after several repetitions of her demand, he responds, "Nearly" (ch. 2). He does not elaborate, primarily because no one wants to hear his thoughts. This is continually revealed in the early chapters of the novel. For example, when asked to "look after the bacon" for Dudley's birthday breakfast, Harry simply groans (ch. 2). His aunt hears his noise, asks what he said, and he replies, "Nothing, nothing." She doesn't urge an answer because she does not truly care what he said.  Aunt Petunia, Uncle Vernon, and Dudley have the majority of the dialogue in the early chapters, as they count Dudley's birthday presents, debate how to leave Harry out of fun events, such as their zoo visit (in honor of Dudley's birthday), and work together to keep Harry's sudden influx of mail away from him. 

Even when Harry does try to speak, his voice is ignored. While the family debates how to prevent Harry from going to the zoo, he suggests that they leave him behind, arguing, "I won't blow up the house" (ch. 2). But his words are again overlooked: "they weren't listening." Soon later, he tells Uncle Vernon, "I'm not going to do anything . . . honestly . . .." Again, readers are told that his uncle "didn't believe him. No one ever did" (ch. 2). When Harry does try to share his thoughts, his extended family immediately rebukes him for speaking. For example, while driving to the zoo, Harry tells his family, "I had a dream about a motorbike . . . it was flying" (ch. 2). Though he was simply making a factual statement about a dream he had, Uncle Vernon angrily retorts:

MOTORBIKES DON'T FLY!

At the start of the novel, Harry's words are ignored, undervalued, silenced, and even rebuked. Humorously, one of Harry's most elaborate conversations early in the novel is with a snake at the zoo. 

I know . . . It [people tapping on your glass] must be really annoying . . . 
Where do you come from anyway? . . .
Was it nice there? . . . 
Oh, I see - so you've never been to Brazil? . . .

The snake responds in gestures to Harry's questions- that is, until Harry accidentally uses magic to free the snake. Then, the snake seems to speak to Harry in actual language, saying, "Brazil, here I come . . . Thankssss, amigo" (ch. 2). The fact that one of the longest conversations that Harry has in the first few chapters is with a snake shows how little his family cared about his words; because he grew up with people who did not value him, Harry begins the story saying very little. 

In chapter three, Harry begins to receive mail, unexpectedly. His family works together to keep this mail away from him; they seem afraid of what the letter might say. Because he was not used to receiving material things and gifts, including mail, he grows frustrated with their interceptions. He shouts out,

I WANT MY LETTER!

Uncle Vernon responds, "OUT!" (ch. 3)

Though Harry makes a bold attempt at speech in this scene, he is again silenced. When other changes begin to happen, such as Harry being offered "Dudley's second bedroom," Harry questions the decision. His uncle responds, "Don't ask questions!" again silencing his voice. Continually, Harry's voice is minimized and silenced at the start of the book. Because of this, he learns to remain quiet. 

In chapter 6, as Harry boards the train for Hogwarts, we see how quiet he is with fellow students at first. He's learned to keep himself quiet from his interactions with his family. When Ron asks if anyone is sitting in his compartment, because the rest of the train is full, he replies by "sh[aking] his head," rather than talking. As the twins come in and introduce themselves, Harry doesn't say anything except, "bye." And, when Ron asks if he is really "Harry Potter," he responds by nodding, rather than words. It takes several paragraphs for Harry to begin talking with Ron and other students.

Even at Hogwarts, some characters try to quiet and minimize Harry's voice and ideas. For instance, when he goes to Potions class, he meets Professor Severus Snape, who questions his magical knowledge and attempts to point out his lack of learning: "What would I get if I added powdered root of asphodel to an infusion of wormwood?," he asks Harry. Harry replies, "I don't know, sir" (ch. 8). Even after he leaves the Dursley's home, Harry's voice is till ignored or belittled by some characters at Hogwarts. Overall, though, friends such as Ron, Hagrid, and Hermione start conversations with Harry that reveal to him how much his voice matters.

Through his friendships and his relationships with professors at Hogwarts, Harry learns to value his ideas and his voice. This is seen at the end of the novel when Harry decides to risk his well-being (and his ability to stay at Hogwarts) to make sure that Voldemort did not get access to the sorceror's stone. Even when he faces the threat of expulsion, Harry tells Hermione and Ron, "I'm going out of here tonight and I'm going to try to get the Stone first" (ch. 16). When his friends challenge him, he shouts,

SO WHAT? . . . Don't you understand? If Snape gets hold of that stone, Voldemort's coming back! . . .

By the end of the first book, Harry has learned the value of independent thinking. He learns to voice his ideas, not allowing others to make him doubt himself. 

Harry grows from being an insecure boy who has been told all his life that he is an unimportant nobody to being a person who gains confidence and happiness. 

In muggle world, Harry is treated as oddity, and apparently has no friends. He is a lonely, neglected, emotionally abused outsider who is bullied and forced to sleep in a closet-like room under the stairs. The Dursleys fear him, because they know his history.

In wizard world, Harry Potter is famous, and he finds a level of friendship and belonging at Hogwarts School that he never knew before. For the first time in his life, he is happy. 

With good mentoring, friendship, love, and encouragement, Harry gains confidence. Instead of putting him down, many people at Hogwarts praise him. Hermione, for instance, says to him:

Harry - you're a great wizard, you know.

Because of this acceptance, Harry has the courage to face evil in the form of Voldemort.

Harry begins the story as a very insecure young boy; he has been mistreated and neglected by his aunt and uncle.  He also does not really feel as though he belongs any where.  As Harry meets Hagrid for the first time, Hagrid is shocked to discover that the Dursleys have never told Harry anything about his true potential

“Do you mean ter tell me," he growled at the Dursleys, "that this boy—this boy!—knows nothin' abou'—about ANYTHING?" (chapter four)

Learning that the was part of a secret world of magic astounds Harry, but he accepts his new role, gladly relishing the chance to be a part of something and learn about who he really is.  Identity becomes an important theme in Harry Potter and the Sorcerer's Stone.  Ultimately, Harry comes into his own and begins to trust himself and his new friends by the end of the novel when they must make their way past the challenges and obstacles lying before the philosopher's stone. 

In this first Harry Potter book, Harry is on the initial part of his journey of self-discovery - learning about who he is, his background and his purpose in life. This journey is developed throughout the remaining books, tracing Harry's journey to adulthood.

In addition, he learns the importance of teamwork and friendship - without which he would not have found the Sorcerer's stone.

Harry Potter experiences quite a transformation in the first book, Harry Potter and the Sorcerer's Stone. In this first novel in the famous magical series, Harry Potter is introduced as a malnourished and emotionally abused child who is living with the Dursleys, his biological aunt and uncle and horrid cousin, in a rather boring English suburb. Harry, who has a peculiar lighting-shaped scar on his forehead, is living with the Dursleys because his parents tragically died when he was just a baby. The Dursleys treat Harry with disdain and cruelty. On Harry's eleventh birthday, that the Dursleys intentionally do not celebrate, he is introduced to the secrets of his past and his wizardly powers by Hagrid, the groundskeeper of Hogwarts, who is tasked with finding Harry and escorting him to Hogwarts. Once Harry learns that he is a wizard and that his parents were killed by the evil wizard, Voldemort, he sets off to Hogwarts with Hagrid to further discover who he truly is and to hone his magical abilities. This is the first major transformation for Harry. Once Harry arrives at Hogwarts, he soon realizes that he is very unique, even among other magical people. While he makes two very close friends, as well as a couple enemies, Harry soon is thrust into a confrontation with the dangerous Lord Voldemort, who is attempting to kill Harry and return to power. This is the second notable transformation for Harry, in which he must learn to use his powers to fight against Voldemort. He soon learns that he will not be able to be a normal young wizard like his friends as long as Voldemort hunts him.

How does Harry Potter's character evolve in the Sorcerer's Stone?

In the beginning Harry is introduced as an ordinary, quiet, reserved, and insecure young boy whose adoptive family mistreats and neglects him to the point of abuse. Aunt Petunia and Uncle Vernon treat him more like a servant rather than a family member, and his spoiled cousin Dudley constantly bullies him.

Soon, however, we learn that Harry is anything but ordinary. The day Hagrid reveals to Harry that he is, in fact, a wizard, marks a turning point in Harry's life. As he learns to navigate his new life as a magical person, Harry's character slowly and gradually transforms and he becomes much more confident and comfortable with himself. When he was living with his aunt and uncle, Harry usually kept to himself because he believed that his opinions and feelings didn't really matter. When he meets Ron, Hermione, and the rest of his new friends, he realizes that he has an important voice and the freedom to express himself freely. There are some people who still give him trouble, such as Draco, but Harry knows how to deal with them because he got a lot of practice with Dudley.

His experiences with his aunt and uncle, essentially, made him mentally stronger and transformed him into someone who truly knows how to appreciate love, kindness and friendship, His early years also made him value loyalty and bravery. When he enters the magical world, Harry finally feels that he actually belongs somewhere and finds the home he was desperately yearning for. He learns who he truly is, but, most importantly, he learns who he can become. Harry's humanity and his ability to give and receive love, makes him a worthy, capable and dangerous opponent of the Dark Lord.