In my opinion, the most important lessons Buck learns in the whole book are the ones he learns from the man in the red sweater.  This lesson really prepares him for the rest of the things he has to face.

When the man beats him, Buck learns that you have to wait until you are able to win before you begin to fight.  You can't just blindly attack out of anger or bravery.

This lesson really sets Buck up for the rest of the story.  He watches and learns so that he can grow stronger and stronger.  Because he knows how to learn from his experiences, he eventually becomes a real power in his world.  If he had not learned from the man in the red sweater, he would have not lived to become so strong.