Some themes of Fitzgerald's novel relate to ideas of moral corruption, materialism, dream and fantasy, and deception.
Moral Corruption: The characters in the story, including Nick, are often duplicitous, exempting themselves from moral responsibility. While Nick merely defends himself through a pretense of innocence and detachment, Tom, Daisy, and Jordan each and all deny responsibility through flight. Gatsby attempts to steal another man's wife, lives the life of a bootlegger and a fraud, yet feels no moral compunction whatsoever. His dream exempts him from responsibility.
Dream and Fantasy: This dream can be understood as a version of the "American Dream", a vision of self-improvement and upward financial/class movement. Gatsby's achievements, though founded in fraud and deception, are nonetheless related to this "American Dream".
Gatsby rises, only to fall, but succeeds in procuring a mansion and massive wealth, which his father remarks upon at his funeral.
Beyond the "American Dream" there is also a theme of fantasy. Gatsby is the primary example of this, as he insists against reason that the past can be repeated. However, Gatsby is not the only character involved in attempting to live out a fantasy.
Daisy and Myrtle both engage in love affairs (at different levels, obviously) that are driven by a vision of romance, which is best understood as a generic ideal of "perfect love" (critically underscored by the presence of extensive wealth).