American Ballet Theatre’s six-week engagement at the Metropolitan Opera House opens and closes with Swan Lake—eight in June; seven in July. The first of Tchaikovsky’s three great ballet scores, it was his most romantic and also his least favorite. When the composer finally heard the ballet Sylvia, written with such a light touch by the Frenchman Léo Delibes and premiered a year before Swan Lake—he told a friend, “Had I known of this music, I would have never written Swan Lake.” And yet, it is still Swan Lake that spells B-A-L-L-E-T to most people. Giving us a chance to hear what Tchaikovsky so admired, ABT performs Sylvia from July 8 to 12, a production divinely choreographed by Sir Frederick Ashton in 1952. The incomparable Giselle, the abstract Woolf Works (based on scenarios from Virginia Woolf’s writings), and Christopher Wheeldon’s Shakespearean The Winter’s Tale round out the season. —Laura Jacobs