Chapter 1: "'Well, to make it short, we want you to do it again.'"
This quote is important because it is what sets the entire novel in motion. Brian is being asked to go back into the wild and show Derek how he managed to survive the previous year. Derek wants to use Brian's knowledge and teaching to teach others how to survive if they get thrown into a similar situation.
Chapter 3: "To want to go back was insane."
This quote shows that Brian is not thrilled about the idea of going back. He is interested in helping others learn from his experience, but Brian knows how horrible it was the first time and has zero desire to repeat the process.
Chapter 7: "'That's what nature is, really—getting food.'"
This quote does a nice job of encompassing the most important lesson that Brian learned from his time in the wild. Food means survival. Without it, you die. It shows perhaps a bit of a cynical attitude, because for many people nature is all about relaxing and beauty and harmony and balance. To Brian, it's none of those things. Nature is a struggle, by every creature, to find enough food to survive one more day.