Nick actually sees Gatsby for the first time at the end of Chapter I, but he doesn't speak to him. It is nighttime. Nick sees his neighbor standing in front of his imposing mansion in the moonlight..
I was not alone--fifty feet away a figure had emerged from the shadow of my neighbor's mansion and was standing with his hands in his pockets regarding the silver pepper of the stars. Something in his leisurely movements and the secure position of his feet upon the lawn suggested that it was Mr. Gatsby himself, come out to determine what share was his of our local heavens.
Nick thinks of introducing himself and then decides against it.
. . . for he gave a sudden intimation that he was content to be alone . . .
Nick sees Gatsby do something rather strange. He stretches his arms out toward the water and appears to be trembling. Nick can see nothing out seaward except a single green light. This light is mentioned several times throughout the novel. It is a light on the dock at Daisy's home in the upper-class section of Long Island. For Gatsby it symbolizes everything he aspires to have, including high social status, good breeding, and, of course, Daisy herself, who represents all the other things.
Nick doesn't meet Gatsby until Chapter III, when he is invited to one of Gatsby's big parties. He finds himself talking to Gatsby without realizing who he is. Nick's impression of his host is a mixed one. Gatsby appears to be friendly and exceptionally understanding. He has an unusually warm smile. But then Nick sees a different Gatsby.
Precisely at that point it vanished--and I was looking at an elegant young roughneck, a year or two over thirty, whose elaborate formality of speech just missed being absurd.
Nick will continue to think of Gatsby as "an elegant young roughneck" who is trying to become an aristocratic gentleman, both in order to win Daisy and to realize his lifelong ambitions to achieve financial and social success. Gatsby has had to be a roughneck because of the way he makes his money. He is involved in a lot of criminal enterprises and has to deal with tough competitors. His friend Meyer Wolfsheim symbolizes the other world that Gatsby belongs to. He is a complex character, with one foot in society and one foot in the underworld. On the one hand, he is hard-headed and realistic, while on the other hand, he is an idealist and a dreamer.