Who are the main characters in Markus Zusak's The Book Thief and what are their goals and conflicts?

Two main characters are Liesel and Max, who both desire to belong and be free.
The protagonist of The Book Thief is Liesel. Her first goal is to get parents. Because her father is gone and her mother seems to be a Communist, Liesel and her brother are sent to live with the Hubermanns as foster parents, but her brother dies on the train. Liesel’s second goal is to learn how to read, as she finds refuge in words and books. She learns how to read by stealing books, which is the origin of her nickname Book Thief.

She hadn’t learned to speak too well, or even to read, as she had rarely frequented school. The reason for that she would find out in due course (Chapter 1).

Liesel finds belonging with the Hubermanns. She has a family at last. In Hans’s loving arms, Liesel learns how to read. Liesel’s other conflict is the individual vs. society conflict of World War II, especially since she has befriended a Jew hiding in her basement.
The individual vs. society conflict of World War II also affects Max, the Jew hiding in Liesel's basement. Max’s conflict is that he is fighting for his life. He is Jewish, and therefore outlawed. The Hubermanns are sheltering him in their basement, and he tries to keep a positive outlook. Max feels the conflict with Hitler is personal, which is why he imagines himself in fisticuffs with Hitler.

“Come on, Führer,” he said, and this time, when Adolf Hitler set upon his Jewish counterpart, Max stepped aside and plunged him into the corner. He punched him seven times, aiming on each occasion for only one thing.
The mustache (Chapter 34).

Max fulfilled his wish to live life on his own terms by going outside at night during air raids, and by leaving even though it was at great risk to himself. Even when caught, Max was still himself. Max was a survivor. He lived because he was creative and positive.