When I first became aware of Leonard Cohen in the 1960s he was known, even to his fans, as Laughing Len.

It was not a nickname I thought fair and I used to argue vehemently it was unjust. But, privately, I had to concede the Canadian minstrel was not the kind of singer-songwriter to send you on your way rejoicing. With a voice that was deeper than a bottomless pit and lyrics that were on the liturgical side of depressing, he was the antithesis of San Francisco-style flower power.

Like Woody Allen, or Randy Newman, or Bob Dylan, Cohen seemed to be wrapped up in angst of his own making. He did not sound like someone who wanted to entertain; rather, he wanted, in his austere manner, to probe what it means to be human and what the purpose of life is. It is not easy, and certainly not commercial, to encapsulate all that into a two and half minute pop song.

This is the Cohen Liel Leibovitz gallantly attempts to explicate in this illuminating critical biography. He fastens on three aspects of his subject's hinterland. The first is his Jewishness. Like Philip Roth, Cohen's relationship to the religion of his forebears is ambivalent. The world in which he grew up in the 1940s was, as Leibovitz points out, almost entirely Jewish. His father, who was wounded in the First World War, was a broken, disappointed man who died, Cohen recalled, "spitting blood, wondering why he wasn't president of the synagogue".

His son was slated to follow him into the family textile business, but that was not to be. What Cohen did inherit was the millstone of being part of a race that was "chosen" by God. But chosen to do what? And why? One imagines these questions haunt him still.

The second aspect on which Leibovitz focusses is Cohen's nationality. He is a Canadian and proud of it. Born in Montreal, he came of age when it was still possible seriously to argue whether there was such a thing as Canadian literature. For Cohen, two very different Jewish Canadian writers - the poets Irving Layton and AM Klein - were formative. Another, the novelist Mordecai Richler, was provocative. Writing in a Canadian magazine, Richler argued "the best influences in the world reach us from New York" and that "the longest unmanned frontier in the world is an artificial one and I look forward to the day when it will disappear."

Cohen read these remarks while in exile in Greece and was riled. He defined himself as Canadian and felt that a denial of one's nationality was prompted by insecurity and a fear of being labelled hicks. Comparisons with Scotland today are so obvious they need not be laboured. Cohen said he would like to punch Richler's nose. "Unless we explore our own possibilities - these things we consider corny - then we'll lose something valuable."

The third, and perhaps most vital, aspect of Cohen to which Leibovitz turns is his poetry. Long before he ever appeared on stage with a guitar he was known as poet. His first collection, Let Us Compare Mythologies, appeared in 1956, shortly after he graduated from McGill University. His second, The Spice-Box Of Earth, came five years later. Both were infused with the spirit of duende, which Federico Garcia Lorca - on whom Cohen doted - described as "a stammer, a wavering emission of the voice, a marvellous buccal undulation that smashes the resonant cells of our tempered scale..."

Duende was what distinguished Cohen as a poet and, later, as a performer. His songs, like Dylan's, seem to have existed in the ether before he found them and put them on albums. Moreover, Cohen himself appeared to speak of things with a timeless, placeless, mystical authority. He was a leader, Field Commander Cohen, in charge of a band called Army, singing of war and armageddon, angels and pain, love and hate.

As he has grown older he has become a guru, for whom crowds will turn up simply to bear witness to his presence. All are eager to hear him intone Hallelujah, of which says Leibowitz, there have been an "obscene" number of cover versions, not one of which, needless to say, compares with the original.