Yes, there are a number of books that address the American dream from various theoretical perspectives. One that directly addresses the question is Jim Cullen's The American Dream: A Short History of an Idea that Shaped a Nation. It is about 10 years old, but it provides a solid overview of how the ideal of the American dream influenced people throughout the nation's history.
Hendrick Smith's Who Stole the American Dream? is more recent. It is an economic perspective on how this longstanding dream has faltered in recent decades. It's more narrowly focused.
Rank, Hirschi, and Foster's 2014 Chasing the American Dream combines an economic approach with a sociological one. It examines social mobility, specifically how people rise and fall economically.
If you combine all of these, you'll have a range of sociological, historical, and economic perspectives on the American dream, and be able to put specific representations of the dream in context.
I'm not sure what you mean, but The Great Gatsby has a huge emphasis on The American Dream.
The original idea of The American Dream was the idea of money. Immigrants would come from all over the world to America to make a successful living. The main character, Jay Gatsby, is very wealthy. He has everything he could ever want except for the girl of his dreams, Daisy Buchanan. He throws all of these extravagant parties in the hope that Daisy will one day attend.
However, it does not end well. I think Fitzgerald, the author, is illustrating that money is not everything in order to achieve The American Dream. Gatsby never gets Daisy but ends up getting killed. It shows that New Money and Old Money can never be together.
Thank you a lot!!!!