Among the last coherent or near-coherent letters that Nietzsche wrote were those to Cosima Wagner, by then the widow of the great composer, in which Nietzsche addressed her as ''Princess Ariadne''; he declared the author of the letters to be none other than the god Dionysus. It is with these extraordinary letters and the poems of the ''Dithyrambs of Dionysus'' that Kohler, also the author of a full-scale biography of Nietzsche, begins ''Nietzsche and Wagner.'' As Nietzsche became steadily less sane, Kohler writes, so he recklessly identified with different selves ''and, like Dionysus, his role model, exchanged one persona for another at will. At one moment he saw himself as Shakespeare or Caesar, at the next as King of Italy or as Wagner, a mortal enemy he pursued with all the savagery he had at his command. And these figures all revealed themselves to him as incarnations of the one god, the god Dionysus, with whom he knew himself to be identical.''

That, however, prompts the question of why Nietzsche chose to dramatize his growing detachment from reality in such terms. Cosima Wagner was one of the 19th century's least likable heroines, proverbial for her gawky appearance and her infinite selfishness, and a far cry from the beautiful and self-sacrificing Princess Ariadne. Kohler's answer is that the villain of the piece is not she but Wagner. Richard Wagner was indeed the ''Old Minotaur'' that Nietzsche called him; he lured Nietzsche into a dysfunctional household of such labyrinthine complexity that it is little wonder that Nietzsche became increasingly wild and erratic.

''Nietzsche and Wagner'' might be described as Nietzsche for beginners -- that is, without philosophy -- though it is hardly Nietzsche without tears. The bare-bones account of Nietzsche's life begins not so much with his birth in 1844 as with the death of his father five years later. Carl Nietzsche was a Lutheran pastor who died of ''softening of the brain,'' which sounds very like a dementia caused by the syphilitic infection that killed his son. Responding to his mother's urgings, Nietzsche became a child prodigy, and he also began to suffer from the nightmares and headaches that plagued him all his life.

What brought him to the state of ardent discipleship in which he met Wagner in 1868 is obscure. He had known about Wagner from his teens, but had disliked the music even while he admired the mythic themes of operas like ''Tristan und Isolde'' and tried himself to write an opera based on Nordic legends. It is clearer what he admired once he had become intoxicated: Wagner promised to re-create for the Germans the cultural climate in which the classical Greek world had created the tragedies of Aeschylus. It was this that ''The Birth of Tragedy'' spelled out in 1872 to its astonished readers.

Politically, it was a view with some alarming consequences, of which Wagner's rabid anti-Semitism was the most obvious. Kohler thinks that Nietzsche was as bad as Wagner in this regard. Both despaired of, and despised, the comfortable bourgeois society in which they lived; both harbored astounding visions of its destruction in torrents of blood and its replacement by a society in which godlike heroes treated the masses with a kindly contempt. As to why the age seemed so indifferent to these archaic heroic ideals, the answer was that a Jewish spirit of commercial moneymaking had rotted German culture.