His angular melodies and dissonant harmonies shook the jazz world to its foundations, ushering in the birth of "bebop" and establishing Monk as one of America's greatest composers. Yet throughout much of his life, his musical contribution took a backseat to tales of his reputed behavior. Writers tended to obsess over Monk's hats or his proclivity to dance on stage. To his fans, he was the ultimate hipster; to his detractors, he was temperamental,...