An informal history of the Metropolitan Opera crosses the footlights in the old and new house to tell of backers, managers, artists and opera. There is panache aplenty in this compendium, from the name society who drew for boxes in the old house (""hardly a music lover in the lot"") through feuding prima donnas and tenors. Miss Eaton has more consideration for managerial reigns than earlier histories (she will have to compete with Irving Kolodin's history, revised in 1966 for an audience), gives the tone, the high points and low of the tenures from Gatti-Casazza through Bing. She sets her stars in the firmament of the Met with precision, characterizing careers, qualifications, and relations with management and colleagues. Not an inside Job, but Miss Eaton (of Opera News) has done her homework and writes with some authority. Only the style is noncommittal.