The name ""Barbarossa"" conjures up, to the Western mind, the terrible figure of Frederick, the German Emperor of history and legend. There was, however, another Barbarossa, one yet more formidable and, more to the point, of perhaps greater significance in history; he was Kheired-Din, ""Protector of the Faith,"" ""Lord of the Sea,"" Admiral of the fleet of Sultan Suleiman the Magnificent, founder of the Kingdom of Algiers -- and undoubtedly an altogether splendid pirate, wino was the terror, and the absolute ruler, of the Mediterranean in the sixteenth century. Mr. Bradford unfolds what is known of Barbarossa's career with a sympathetic verve, a thoroughness of research, and a narrative style which makes of this, the first full-length treatment in English of that much maligned Turk, one of the most unusual and fascinating historical popularizations to appear this year. The scholar will perhaps balk at Mr. Bradford's habit of quoting comtemporary chronicles. European as well as Muslim, without citing his sources, and of running together conjecture and fact so that, for the general reader, one is hardly distinguishable from the other. Be that as it may, the less critically inclined reader will find The Sultan's Admiral highly informative and hugely entertaining.