Born in St. Petersburg, Russia, in 1904, George Balanchine was the 20th century's towering figure of classical ballet. Coming to America in 1933, Balanchine founded the School of American Ballet and the New York City Ballet, where he hired the Danish-born Peter Martins as a dancer and, later, as a choreographer. Balanchine and Me is dedicated to Martins's profound artistic relationship with George Balanchine, who taught him a new, freer style of dance,...