Analyze how The Great Gatsby challenges the established values of its time.

In many ways, The Great Gatsby is a quintessential example of life in the 1920s, the era in which the novel is set, but Jay Gatsby, one of the main characters, challenges the values of the era with his approach to wealth.
Gatsby shares his wealth by throwing extravagant parties and welcoming everyone. He makes everyone feel as if he is fond of them and wants them around. Gatsby wants to be liked more than he wants to be rich but has no problem using his wealth to make people like him. Later in the novel, we see that he is willing to go to extremes to be loved as well.
Compare this to the stiff, reserved representations of "old money" in the novel, like Tom and Daisy. They aren't nearly as welcoming to Nick as Gatsby is, even though they've known Nick longer. While they invite Nick to their home, they aren't nearly as hospitable or welcoming as Gatsby is. Tom and Daisy are used to the idea of being wealthy, and while they know their money can be used to their benefit, they're reserved in regard to their lifestyle and privacy, keeping secrets of their marriage from even those close to them.
Gatsby, on the other hand, makes a show of his wealth by throwing parties and treating his friends to outings. While Gatsby keeps secrets, he does so to make himself more amiable, and he feels that he has more to lose if his friends stop liking him. Essentially, The Great Gatsby challenges the 1920s values of conservatism and wealth.