Part 4 is an important section of The Book Thief because it is when Max first arrives at the Hubermann household. Max's introduction to the household and the friendship he develops with Liesel helps both of their characters evolve to deal with the uncertain, changing world around them.
Walter Kugler, the man we saw in Part 3 helping the Jew named Max, shows up at the Hubermann household to talk with Hans. He asks about Hans' accordion playing and we learn that Hans learned to play from a Jew in World War I, named Erik Vandenburg. Erik helped save Hans' life too, by getting him a job that kept him out of a terrible battle. Kugler asks if Hans remembers his promises...
Max (who turns out to be Erik's son) first arrives on Himmel Street in November of 1940. We learn about Max's past: he's a German Jew and a fist fighter, who has dealt with the problems in his life by fighting. When his problems became more abstract (the Nuremberg Laws stripping him of citizenship, the guilt of leaving his family overwhelming him, the struggles of living in hiding for 2 years already before coming to the Hubermann's house) Max still finds ways to fight back.
When Max arrives at the house, he eats a bowl of Rosa's pea soup too quickly and gets sick. Liesel is surprised to see Rosa concerned about Max and realizes there is more to her foster mother than she thought.
Hans tells Liesel his history with Max's father, Erik, and tells her she must never tell anyone Max is staying with them.
Liesel watches Max sleep for three days, during which he has nightmares and seems to be struggling with someone or something. She feels a connection to him, as they were both taken in by Hans and Rosa and both are haunted by nightmares.
Max is moved to the basement for everyone's safety, where he paints over a copy of Mein Kampf to write The Standover Man - his own struggle during the reign of the Nazis.