Some of things you should take away from this novel:
The character of Jay Gatsby symbolizes some of the false aspects of an American Dream gone awry. Instead of focusing on self-improvement and empowerment through financial betterment, Gatsby focuses on using his wealth to fulfill a fantasy. His fantasy is almost purely romantic and he uses this romantic ideal to justify his criminal behavior and his many lies.
There is an idea in the novel, however, that some lies help point to larger truths. Gatsby and the narrator, Nick, both engage in some lying about themselves but these lies help to define their aspirations. They want to be honest. They want to be educated. They want to be sophisticated. So they tell people that this is who they are, hoping that in telling the lie they can come closer to making the lie into the truth.
Money cannot buy happiness and crime cannot wipe out innocence. These are two concepts explored in the novel.
Topically, the novel explores the society of the wealthy in America and juxtaposes their experiences with those of the lower classes (George and Myrtle Wilson), depicting the great divide of potency between them while also connecting them through a shared set of values (money as the ultimate "good").
This novel is a nice example of modernism in that the narration is marked by subjectivity, the characters are well-developed yet bear some symbolic significance at the same time, and certain passages are rendered impressionistically.
Though the novel is broadly cynical, it is also hopeful in its poetry and stands as a rather beautiful reverie concerning how we come of age in America and sift the true from the false in our lives and in our selves.