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When we first meet Müller, he seizes the opportunity to take Franz Kemmerich's soft leather boots with him when Kemmerich is about to die. Müller has no shame about showing his more base, selfish feelings and desires. While the reader is initially shocked and appalled by his behavior, we realize pretty soon that he's doing what every guy has to do to survive in the war—looking out for #1.
Müller's not just a soulless pragmatist, though: he's also a dreamer. He's one of the few men who actively thinks about the future, even going so far as to ask the question:
"What would you do if it were suddenly peace time again?" (5.4)
He becomes obsessed with the question and forces each of his mates to open up, physically confronting them if they hesitate to answer. He's also the one who leads the mockery of the "silly" things they learned in school, asking trivia questions of the guys as if they were still in school. The irony of the meaninglessness of these questions against the backdrop of basic human needs in the war defines Müller's tone. He dies from a shot of a light pistol in the stomach. He survives half an hour in terrible pain, handing over his precious boots to Paul during his last minutes.