For more than fifty years we - all of us - have been trying to make sense of the Holocaust, trying to find a rationale for history's first act of genocide, some way into the horror that no one, maybe not even the Germans, was prepared for. For Israelis it led to the phrase 'Never again!" But for the governments of Serbia, Rwanda and Cambodia the Holocaust was a pretty good idea. Nothing has come along since to close the door on it, and that is why a film like Roman Polanski's "The Pianist," made from Wladislaw Szpilman's memoir, is so important.

Szpilman, played here by Adrien Brody, was an upscale Jew in Warsaw before the war, a Chopin specialist on the radio, and even had a jazz band on the side. He and his family were secure until the Germans invaded; the film is the record of his life and survival during the war. Little by little the Germans closed the noose around the Jews, moving them into a ghetto, beating and humiliating them, shooting anyone with or without a reason, denying them even the basics of life. Szpilman, as we see him here, is not a fighter; he thinks of himself as someone who will survive because he is an artist, and art will survive. He's offered a chance to join the Jewish police, who at least get little favors from the Nazis, but declines; and then his friend, who did join, pulls him from a train to Treblinka and saves his life. "Run," he says, and Szpilman does.

He runs, and he hides, and is helped by gentiles in the resistance, and grows weaker and sicker and more animal-like than he ever could have imagined in his previous life. But he survives. At one point he finds himself hidden in a safe apartment with a piano; but he cannot play it for fear of being discovered, so he fingers his Chopin above the keys and listens in his mind to the music he's making. And then late in the film and the war, he is discovered hiding in the attic of a building the Germans have taken over; in a quiet and breathtaking scene the captain (Thomas Kretschmann) tells him to sit at the piano and play for him. In the cold room, with his breath visible, Szpilman plays for the captain, not knowing what will happen. Polanski has given us a memorable moment.

Others have pointed out that the story of a survivor is in fact the rare exception, the oddity, because the fate of almost all Jews in Poland was to die. Most died in the death camps or along the way; the rest died in the resistance, in the ghetto uprising of 1943, died in the vain hope that the Allies would come to their aid. Polanski's film contains all of this, opens itself to every implication we can take from the Holocaust. Perhaps the most powerful part is the first hour, when his film records in excruciating detail the slow and inexorable march to death of Jewish life in Warsaw. Polanski's command of his material and his actors, and his understanding of how people walk and look and speak and die and kill is astounding here, and we flinch at everything we see. Every shot is a masterpiece of composition and lighting and choreography - the shuffling of thousands of Jews being herded here and there, the odd word of comfort, the unexpected and random deaths - all are classics of cinema.

The rest of the film, sticking close to Szpilman in his various hiding places, is fascinating in another way. Szpilman is not a hero, looking for a glorious death, determined to fight and die, or at least to fight. He is weak, self-absorbed, acting only in order to survive another day, to run away from death, to hide. Polanski, who as a child in Poland did the same thing - his father pushed him under a barbed-wire fence and told him to run - understands better than we just how and why Szpilman acted as he did.