We learn quite a bit about Nick Carraway, and a bit about Gatsby, in the third chapter.
In this chapter, Nick attends one of Gatsby's parties for the first time. We learn that it is important to him that he was invited, suggesting that he differentiates himself from the random gate-crasher who is a typical Gatsby guest. We also learn that, as Nick puts it,
I found it necessary to attach myself to someone before I should begin to address cordial remarks to the passers-by.
This throws him into the company of Jordan Baker, the only person he knows, at least slightly, at the party. From this encounter, they will form a more intimate relationship.
We also discover, when the two meet for the first time, that both Gatsby and Nick served in World War I and had seen one another there:
"Your face is familiar," he [Gatsby] said, politely. "Weren’t you in the Third Division during the war?"
"Why, yes. I was in the Ninth Machine-Gun Battalion."
"I was in the Seventh Infantry until June nineteen-eighteen. I...
(The entire section contains 2 answers and 690 words.)