It's well known, that the "Sorcerer's Stone" was written by the author for her little daughter, who enjoyed the stories about a little wizard boy. Rowling confesses, that all of the characters in her books have been written from her friends, former classmates and teachers, and from Rowling herself. Both of those books are about the wizarding world, which is very near to the mundane one, but humans don't notice it. "The Sorcerer's Stone" and the "Goblet of fire" describe the stages of the main protagonist's growing up. These books tell about the hardships a person who grows up without parents has to come through, they emphasize the need in close people Harry feels.
Both of the books tell about different stages of growing up. It's well known that teenage years are a period when a person learns to decide for himself or herself and to take responsibility for his/her decisions. Both "The Sorcerer's Stone" and the "Goblet of fire" feature teens and tweens who have to decide complicated problems, which are often of grave importance both for them, their classmates, and sometimes, even for the whole wizarding world.
The books discussed talk about the importance of making the right choice, the one that is dictated by your heart and mind instead of the one that is suggested by fear. The importance of acting according to the one's moral principles regardless of the value is the key concept for both of those books. The protagonists act guided by the eternal values the ones that most of us would like to engraft to our children, but we don't know how. The positive characters depicted in these two books are guided by friendship, love, care about the surroundings and self-respect. They aren't taught to compromise when those matters are touched, and they don't want to learn how, as like all of the teenagers they yearn for the extremities.
The common topic in "Harry Potter and the Sorcerer's Stone" and "Harry Potter and the Goblet of Fire" is also the relationship between people. Rowling displays the importance of establishing and maintaining close friendly relationships with those, who surround you. It is clear in both of the books that without the help of Ron, Hermione and some other creatures Harry couldn't have accomplished the tasks he had to accomplish.
One of the leitmotivs that connect two of the books discussed is that struggle Harry leads with his name. For most of his surroundings he is "that famous Potter, the boy that survived". It seems to him that people expect much more of him that he is able to accomplish. One of Harry's fears is that people will percept him only as "the boy, who survived", or "The boy who was very lucky". He does his best for to prove that he is worthy of love and respect not only because of the scar on his forehead, but also because of his outstanding capacities in problem solving, his courage, loyalty, and intelligence.
Of course we shouldn't forget that both of the books we discuss are also about education. Considering the fact that unlike in the ordinary schools in Hogwarts people are taught how to use practically their natural capacities, we can note that both books are about the initiation, the development of the powers that existed inside the person from the moment of his/her birth.
As you see, there are