Here are the elements:
AzkabanEXPLANATION 1: Harry Potter is a Marxist tract that envisions a common man who stands against the dark forces of capitalism as displayed by the prison, Azkaban. Yes, it is extreme, but all good satire is extreme. Azkaban represents in miniature the horrific conditions that inmates suffer in most Western prisons up to the moment of execution (in the United States). Harry Potter's magical powers symbolize his inalienable rights that are repeatedly challenged by those higher up the social scale. He is supported by the underclass—the house elves—who in their willingness to defend Harry Potter's cause echo the revolutionary spirit of Marxist insurgents; in subjugating their individuality for the common good, they demonstrate what is needed to bring about a new tomorrow.
Harry Potter's magical powers
The house elves
SUBTEXT: Rowlings is a liberal with a liberal agenda. She is using the Harry Potter books to destroy capitalism by promoting a Marxist agenda.EXPLANATION 2: Harry Potter is an Ayn Rand-inspired text. Harry Potter is the ultimate individual who, despite the debased no-thinking/self-imposed slavery of his peers--the house elves--and society--Azkaban, manages to retain a sense of superior individuality through his use of magical powers. Like all good Ayn-Rand heroes, he ultimately becomes a self-created and self-important being: sui generis.
SUBTEXT: Rowlings is a gung-ho individualist who believes that independent spirits will save the future.EXPLANATION 3: Harry Potter is a religious text. Azkaban represents the evil that resides in all men (and women). Note that the Azkaban warders appear when Harry Potter begins to despair. His saving magical powers refer to grace which will save him if he will accept it. The house elves represent good spirits/saints/intentions who remind Harry Potter of the need for humility through their examples.
SUBTEXT: Rowlings is a fundamentalist Christian who is using the Harry Potter books to persuade readers to give up their sins and repent.EXPLANATION 4: Harry Potter is a Horatio Alger text. Harry Potter is the ultimate barrow boy who, with drive and determination, rises above environmental determinism symbolized by the warders of Azkaban, who destroy a person's will to survive and ability to progress. Harry's magical powers symbolize the skills and abilities that not even poverty can hide. The house elves represent what Harry Potter could become if he does not rely on that innate drive and determinism: self-entitled drains on the economic stability of a nation.
SUBTEXT: Rowlings is, despite being British, trying to feed people the erroneous concept of the all-American dream. Everybody knows that immigrants were worse off when they got here! Everybody knows that the streets weren't paved with gold! And now she's trying to sell the idea all over again.EXPLANATION 5: Harry Potter is a feminist tract. Azkaban represents the patriarchal forces of a mostly male-run world. By aligning himself with Hermione, Harry Potter allows his feminine side to show through. Harry himself is not the driving force of the novels; through his magical abilities, he represents the "male" or "power" side of Hermione. The house elves represent the slavery (a la "The Yellow Wallpaper") that all women suffer. Hermione's attempts to "free" the house elves are her attempts to free her own understanding and act for herself.
SUBTEXT: Rowlings is using the Harry Potter novels to preach a feminist message. She made a male the hero because her message, like all good feminist messages, is subversive.EXPLANATION 6: Harry Potter is a deconstructionist text: everything eventually means nothing. By pervading the books with Azkaban imagery, Rowlings prepares the reader for randomness and anarchy. She deliberately creates non-explained phenomenon. She also creates characters who insist on linear progression—the house elves—despite the obvious non-structural aspect of the books; consequently, the house elves remain slaves to Western artistic expectations. Harry Potter, like the characters in Waiting for Godot, exists in a world that he cannot actually act upon; he has magical powers but no power to choose. He is the post-modern hero because he accepts that nothing can be learned or really understood.
SUBTEXT: Rowlings is trying to expose us to the true relativity of life. She does this by subverting ordinary/linear Western archetypes to reveal their basic shallowness.EXPLANATION 7: Harry Potter is a cry for good parenting with, naturally, a Freudian twist! Harry has no strong parental figures in his life. This exposes him to the evils of the world (Azkaban, the boarding school). He has to rely on his own sense of right and wrong (ego). This is made clear by his reliance on his magical powers (the id) rather than on parental teachings (superego). Furthermore, the text is replete with examples of parents who fail to live up to their parental responsibilities, creating a corrupt second generation (Malfoy and his father) that cannot think for itself (the house elves) and must struggle on its own (Hermione and her parents).
SUBTEXT: Rowlings is challenging parents of today to live up to their obligations. By giving Harry Potter a happy marriage at the end of the novels she hopes to break the cycle that Harry Potter was born into.
EXPLANATION 8: Okay, I'll spare you.
All explanations and subtexts are my own. The jargon isn't.