We've only just passed midsummer but this has already been quite a year for Leonard Cohen, the 73-year-old with a reputation for crushing introspective solemnity. In January he announced details of his first tour in 15 years and in March he was inducted into America's Rock 'n' Roll Hall of Fame where he will make an unlikely exhibit beside fellow inductee Madonna. Still, they do at least share a preoccupation with sex.

More importantly, however, Cohen's Hall of Fame induction unites him with Bob Dylan and Joni Mitchell, the two fellow artists he most admires and, in many senses, resembles. Together they form the holy trinity of confessional poet-troubadours; certainly they are the three finest lyricists of the rock age.

Given all that, it's no surprise that news of Cohen's upcoming tour was greeted with something bordering on hysteria. A sell-out from start to finish, it began in May and takes in two opera houses, three castles and a selection of top European festivals.

Among those festivals was Glastonbury, where Cohen took to the stage dressed like an ageing gangster in a double-breasted suit and fedora to perform a 16-song set which included the classics Suzanne, Bird On A Wire, So Long Marianne and Hey That's No Way To Say Goodbye. Among the castles is Edinburgh, where he will perform this week, presumably in the same garb and with the same set-list. That will mean no Chelsea Hotel #2, his famous song about Janis Joplin, and no Famous Blue Raincoat, the painful elegy describing a love triangle in which Cohen, typically, is both loser and winner. Still, you can't have everything.

In fact the thousands of Cohen fans who snapped up tickets for the tour are lucky to have anything at all. The man who disappeared into a Zen Buddhist monastery in California in 1994 and took the name Jikhan - meaning "silence" - gave no indication then that he would ever tour or even record again. Interviewed in 1997 and asked about his intentions, he was anything but positive in that regard. "The devil laughs when we make plans," he said. "I wouldn't want to say never, but I'm not waiting for the phone to ring."

Cohen did finally emerge from the Mount Baldy monastery near Los Angeles in 1999, and once more found his voice and his muse. He has since recorded two albums: 2001's Ten New Songs and 2004's Dear Heather, co-written with his current partner, 49-year-old Anjani Thomas. The lyrics to Dear Heather's title track are classic Cohen: simple, punchy, memorable and cleverly balanced between pain and promise. "Dear Heather," they run, "Please walk by me again/With a drink in your hand/And your legs all white/From the winter." And that's it.

Few songwriters can deliver a story in just 21 words, but then Leonard Cohen is unlike most songwriters. Born into a wealthy Polish-Lithuanian Jewish family in Montreal on September 21 1934, his was a childhood infused with music and religion. The family had been in Canada since 1860, and Cohen recalls his father, Nathan, speaking English with "a Scottish burr". Nathan loved Harry Lauder and Gilbert and Sullivan, and would play their records in the house. When he died in 1944, his nine-year-old son cut open one of his bow ties, wrote some words on a piece of paper, slipped it inside and buried both tie and message in the garden. Recalling that tender act in a 1993 interview, Cohen said: "I know that was the first experience I had with that kind of heightened language that I later came to recognise as poetry."

At synagogue, Cohen would listen to liturgical music and, at home, his mother would sing folk songs in Russian as the family observed the sabbath rituals of prayers, candles and kosher food. Around him, however, was a city dripping with Catholic iconography, and his lyrics would in time come to reflect that twin heritage, becoming suffused with both Christian and Jewish imagery.

In 1951, aged just 15, Cohen entered McGill University in Montreal. Five years later, inspired by Lorca, Camus, Sartre and Yeats, he published his first volume of poetry, Let Us Compare Mythologies. After an abortive year at university in New York, he spent the early 1960s living on Hydra, an island off the southern coast of Greece. There he completed another poetry collection as well as two novels. A literary career beckoned.

But in the mid-1960s he returned to New York and dipped into the Greenwich Village folk scene where he first encountered Bob Dylan, Joan Baez, Phil Ochs and Judy Collins. In 1967, after a military coup in Greece, he relocated to the city and embarked on a career as a folk singer while also penetrating Andy Warhol's Factory crowd. He was in his mid-30s at the time, far older than almost everybody else on the scene bar Nico, who fascinated him and whom he once described as "the perfect Aryan ice queen".

The feeling wasn't mutual. Nico told him he was too old for her, a put-down that would find an echo of sorts in Chelsea Hotel #2, where Cohen sings: "You told me again you preferred handsome men/But for me you would make an exception." That song is included on Cohen's 1974 album New Skin For The Old Ceremony, regarded by many - him included - as his best. But the incident it narrates, a liaison with Janis Joplin in New York's Chelsea Hotel, took place shortly after the release of his first album, Songs Of Leonard Cohen.

From that album comes Suzanne, one of his best-loved and most widely covered songs. Nina Simone roughed it up a little without losing any of its essential mystery, while Sandy Denny and Fairport Convention made of it an ethereal folk song. These are just two versions. There have been many others, though Cohen's, delivered in his trademark baritone, remains the benchmark. The song itself is as much a love poem to Montreal as it is to the Suzanne of the title, the wife of a sculptor friend. It is, like all Cohen's work, grounded in truth. If you know the song, Suzanne did invite him down to her place near the St Laurence river, she did feed him tea and oranges, there is a statue on the sailor's church called Our Lady Of The Harbour on which the sun does pour down like honey.

Between the 1967 and 1974 albums Cohen released two others, Songs From A Room (1969) and Songs Of Love And Hate (1971). Collected together they form the body of work on which his reputation as a lyricist and songwriter rest. Bird On A Wire, Lady Midnight, Sisters Of Mercy, So Long Marianne, Hey That's No Way To Say Goodbye, Chelsea Hotel #2, Who By Fire and Take This Longing all come from them.

so too does his reputation as a bedsit miserabilist. Reviewing his appearance at the 1970 Isle of Wight Music Festival, The Guardian referred to Cohen's "lonely listeners" and his "simple, sad lyrics spiked with a few of those ringing, oracular lines that thrill the romantic young of all ages". The New York Times critic John Rockwell complained about the "constant, lugubrious pall" that hung over Cohen's songs. Ever since, Cohen has been saddled with sobriquets like "the poet of pessimism". It's not a portrait he necessarily recognises. "My reputation for solemnity is ill-gained," he said in a 1992 interview. "They call me Laughing Len in England. They used to say razor blades should be distributed with my records."

It also contradicts his other reputation as a womaniser, though here too he takes issue. "Ladies' man was another title attached to me, as if I were pre-eminent. I've known ladies' men in my life and I'm not even in the ball game," he said in another interview. "These two descriptions together, depressing, gloomy and ladies' man - as if women were really interested in that kind of character."

Today, Cohen's most famous song is Hallelujah, which features on his otherwise unloved 1984 album Various Positions. It has been used on numerous film and television soundtracks over the years though rarely, if ever, in its original version. Instead it was Jeff Buckley's version, included on his 1994 album Grace, which fixed it in the popular consciousness.

In fact Buckley wasn't the first person to tackle it. In 1991, Nico's former Velvet Underground bandmate John Cale recorded it, trimming the 15 pages of lyrics Cohen faxed him into something a little more manageable. It's this version that Buckley appropriated and which has since been covered by KD Lang, Rufus Wainwright, Sheryl Crow and Bob Dylan to name just a few. It recently went to number one on the iTunes download chart after it was featured in the programme American Idol. Cohen, ever the sly showman, included it in his Glastonbury set and will surely play it in Edinburgh.

Cohen tells a story about discussing the song with an admiring Dylan in a Paris café. The American was using Hallelujah in his set and wanted to know how long it had taken to write. The Canadian lied. "I said it took three or four years," Cohen recalled.

"Actually it took longer. And later on in the conversation I praised a song of his called I And I, and asked him how long he took to write it. He said 15 minutes' and I believed him." True or not, it does highlight the difference in productivity between the two songwriters: Dylan has made over 30 albums in his career to date, Cohen has managed just 11.

Of course comparisons between the two men are as invidious as they are appealing. Dylan is a musical polymath steeped in Americana while Cohen, a devoted Quebecois, is far more European and literary in outlook. One glaring similarity, however, is the scrutiny paid to their love lives by both fans and critics. In part this is due to their status as performers, but mostly it's a result of their painfully confessional songwriting. Dylan's Blood On The Tracks album, for instance, analysed the dissolution of his marriage to Sara Lownds, while Cohen's So Long Marianne namechecked Marianne Jensen, the woman he lived with on Hydra.

Cohen and Jensen split in 1968. In the same year, Cohen took up with Suzanne Elrod, an artist from Miami. They had two children together, Adam and Lorca, but by 1977, the year Cohen recorded the ironically titled Death Of A Ladies' Man, the relationship was in crisis. Though not without its fans, the album is a suitably fractured and fractious piece of work, from the rowdy Memories to the bawdy Don't Go Home With Your Hard-On, which features Dylan and Allen Ginsberg on backing vocals.

It certainly wasn't a happy time for Cohen. These were also his drink and drug years and, to top it all, he was writing and recording the album with Phil Spector. "It was clear that he was eccentric," Cohen later recalled, "but I didn't know that he was mad." That he was became clear when Spector pulled a gun on Cohen during a recording session and then insisted on mixing the record under armed guard. "My flip-out was withdrawal and melancholy," said Cohen afterwards. "His was megalomania and insanity and the kind of devotion to armaments that was really intolerable."

Since the end of his relationship with Elrod, Cohen has been romantically involved with photographer Dominique Isserman, actress Rebecca de Mornay and musician Ananji Thomas.

Despite his legendary status, Cohen's stock has fluctuated widely over the years, particularly in the early 1980s when he swapped guitars for synthesisers. His record label refused to release 1984's Various Positions in the US, and it took a 1987 tribute album by his former backing singer Jennifer Warnes to re-introduce him to a younger audience. Cohen made a comeback of sorts in 1988 with I'm Your Man, which includes the songs First We Take Manhattan and Tower Of Song, and had a considerable commercial hit with The Future in 1992, but his five-year retreat curtailed his recording work for the rest of the 1990s.

By his own standards, then, he has been prolific in the noughties, with two albums so far. However, this 2008 tour was born more of necessity than out a genuine desire to see Dublin, Manchester and Edinburgh again. In 2005 he alleged that his former business manager Kelley Lynch had siphoned off $5 million from his pension fund, leaving him just $150,000. Despite a court ruling in his favour, he has recouped none of the money to date.

And so he's back on the road, grafting nightly in castles and opera houses and humbly lifting his hat between songs to say thanks.

"I love talking about the various ways in which I am unappreciated," he once said. The self-styled "worker in song" may be old, grey and skint, but unappreciated he is not. He is a legend, and he doesn't need the Rock 'n' Roll Hall of Fame to tell him so.