George Balanchine, who lived from 1904 to 1983, was the greatest choreographer of the 20th century. This he knew. But just as important to Balanchine was his work—and legacy—as a teacher. In his youth in Russia, Balanchine’s fellow dancers looked upon him as the one who would lead them into a new era. By the time Balanchine got to America, in October of 1933, he was ready to create that era. “But first,” he said, “a school.” The School of American Ballet was founded in 1934. In 1948, after 14 years of short-lived companies, the New York City Ballet was founded. Through all those years, and until his final illness and death, Balanchine taught company class. It was an exploratory education in classical dance and its expressive potential in time and space. “It’s like I was a pupil of Einstein,” said the late Jacques d’Amboise. Connie Hochman’s illuminating new documentary, In Balanchine’s Classroom, goes into the details with NYCB dancers from many generations, and contains never-before-seen archival footage and home movies. On September 17 and 18, at the 6:30 shows, Hochman will conduct in-person Q&A interviews with, respectively, former NYCB stars Merrill Ashley and Edward Villella; tickets are required. —L.J.