Few celebrities are as instantly recognizable as Woody Allen. Few are as notoriously shy. And perhaps none are as elusive: Is Woody Allen a comedian who wants to be taken seriously? Or is he a serious artist whose films happen to be funny? The very fact that Eric Lax was granted access to Woody for four years in order to research this biography must be counted as a triumph. And what Lax has produced is a marvel of intimacy and insight: a book that...