PERHAPS genius can be perceived no way but kaleidoscopically, with interpretation endlessly rearranging the same bright shards. Who was Nietzsche? ''Listen!'' he shouts at the beginning of ''Ecce Homo,'' and the italics are naturally his, he being the emperor of vehemency. ''For I am such and such a person. For heaven's sake do not confound me with anyone else.'' The chapter titles then explain even more about him: ''Why I Am So Wise,'' ''Why I Am So Clever,'' ''Why I Write Such Excellent Books.'' Our immediate reaction, as he might have intended, is to suspect the wisdom, cleverness and excellence of ''such a person's'' books.

Nietzsche was born in Rocken, Prussia, in 1844, and died, having gone insane, in 1900. He was educated at Bonn and Leipzig and was self-educated (and dis-educated) thereafter. But who, really, was he?

Heidegger is onto something when he advises us that philosophy can be possessed ''most purely in the form of a persistent question,'' and that ''Nietzsche's procedure, his manner of thinking in the execution of the new valuation, is perpetual reversal,'' perhaps like life itself, not to mention Heidegger's own devoted explications of Nietzsche. That arch-muse Lou Salomé, who knew him not only as a thought machine but also as a lover of sorts, stated the case more intimately when she wrote, ''In Nietzsche the most abstract thoughts habitually could reverse themselves into the power of moods which could carry him off with immediate and unpredictable force.''

Ecce homo, behold the man! As we peer down time's long barrel to try to see him, his hand keeps turning the kaleidoscope.

Curtis Cate's new biography assists in the beholding, by rebuilding who Nietzsche was out of as many shards as possible, retelling his life in vivid snatches while presenting the labors of his mind. As Nietzsche would have informed us, such a project cannot but be a failure, yet what a pleasing and admirable failure it is! Anyone who summarizes in a handful of pages, as Cate has bravely done, not only each of Nietzsche's books but the relevant aspects of Schopenhauer, Aristotle and others by whom Nietzsche was influenced and against whom he reacted, is asking the world to pick nits. Nits will be picked. No matter. This is a warmly intelligent introduction to Nietzsche.

Any decent biography is a work of drama. What then are the dramatic moments of Nietzsche's life, the ones we most anticipate the telling of and judge the biographer by? Well, obviously the Nietzsche-Wagner friendship and its end is such a moment. The romance with Lou Salomé is another. Then there's the tumble into madness and the relationship with his sister Elisabeth, who disarmingly tells us that ''the fact that I had spent the greater part of my life in the company of so superior a person as my brother robbed me of . . . self-confidence'' and who found the confidence nonetheless to refashion her brother's image to suit her ends. Finally, there's Nietzsche's moment of responsibility, hypothetical or not, for the intellectual climate that brought about National Socialism. How well does Cate do in regard to each of these?

Start with Wagner. Cate brings him alive in all his titanic egotism and ambition. We come to understand, and perhaps to be touched by, the composer's notion that the opera house built to his specifications at Bayreuth could actually raise the level of German culture. In this context, Nietzsche's wavering impulse to sacrifice his philology professorship to stump for Wagner's project makes amusing sense.

Here and everywhere, Cate succeeds in exciting our compassion for his hero. Particularly moving is the spectacle of a savagely independent intellect, whose utterances are so fiery that they should have been printed in red ink, abasing itself to timidly ask the Wagners' permission to play its own composition on the piano, a piece that finds no favor with them.

H. L. Mencken, who wrote an introduction to the published Nietzsche-Wagner correspondence, considers it ''quite possible,'' as Elisabeth opined, ''that it was Wagner's snuffling gabble about Christianity that finished'' the friendship. ''After those walks at Sorrento there was nothing for'' Nietzsche ''to do save make his bow, click his heels together and say goodbye.'' Cate shows that it was over before then, faithfully detailing the gradual widening of the personal, moral and aesthetic gulf between the two men. Liberal quotations help us feel some of the complexities -- for instance, Nietzsche's poignant claim that ''it was the aging Wagner I had to resist: as regards the authentic Wagner, I will to a good extent become his heir.''