Pygmalion (Roundabout/AA, 227 W. 42, closes Dec. 16). George Bernard Shaw’s greatest comedy, lavishly and immaculately revived for the first time on Broadway since 1987. Claire Danes makes her professional stage debut as Eliza Doolittle and belts it out of the park, with Jefferson Mays (I Am My Own Wife) giving a comparably dazzling performance as Henry Higgins, the fanatical phonetician who means to make Eliza a lady by erasing her Cockney accent. Great staging, great supporting performances, great sets, great lighting. Even the incidental music, all of it by Elgar, hits the bull’s-eye. This one is already a tough ticket, but do your damnedest (TT).