I never met any one of his class who remembered him. They did not even remember that he was middleweight boxing champion.
-- Narrator/Jake (Chapter 1 paragraph 1)

Importance: This paints Robert Cohn as a person of little importance who does not fit in, a characterization that will continue throughout the novel.

He was fairly happy, except that, like many people living in Europe, he would rather have been in America, and he had discovered writing.
-- Narrator/Jake (Chapter 1 paragraph 1)

Importance: This presents the attitude held by some of the expatriates who were torn between America and Paris. It also introduces the idea that writing is something to be both loved and dreaded.

Brett was damned good looking. She wore a slip over jersey sweater and a tweed skirt, and her hair was brushed back like a boy's. She started all that.
-- Narrator/Jake (Chapter 3 paragraph 2)

Importance: This establishes right away that Brett is a new breed of woman who is independent and free spirited.

Don't we...
-- Brett (Chapter 4 paragraph 10)