THE appointment of David Greig to lead the capital's great repertory theatre was one of the most audacious moves in the recent history of live drama in Scotland. Greig – who last week announced his first season as artistic director of Edinburgh's Royal Lyceum – is, after all, best known as a playwright, rather than a director.

In appointing him, the Lyceum board is taking a gamble on Greig. Their hope and belief is that he will bring his immense intellectual and creative energy to the running of one of Scotland's most important producing theatres.

When we meet at the grand old playhouse, I half expect him to be exhausted by the process of putting together his amazing, inaugural 12-show season. In fact, I find him as sharply engaged, welcoming and intellectually direct as ever.

"It's about not being afraid to flirt with the existing audience a little and offer them things that are, maybe, a little riskier than stuff that's been on before," he says of his first programme. "However, it's also about going out into the city and bringing new audiences in."

Greig is the perfect person to try to strike this balance. Something of a quiet revolutionary, he is as calm in his demeanour as he is dynamic in his intellect.

Which is just as well, as the 2016/17 season he has in store for Lyceum audiences will raise more than a few eyebrows. There's a theatre-writing debut for singer-songwriter Karine Polwart, in the shape of her music-infused piece Wind Resistance; a staging of acclaimed avant-garde English playwright Caryl Churchill's futuristic drama A Number; and an outing for Austrian author Peter Handke's large-scale, wordless play, The Hour We Knew Nothing Of Each Other.

Greig's opening directorial gambit, which also includes repertoire favourites such as Shakespeare's The Winter's Tale and Noel Coward's Hay Fever, is the work of a man who is steeped in the history and practice of drama.

Born in 1969 in Edinburgh, Greig spent his early life in northern Nigeria (his father worked in the construction industry), returning to Scotland with his family when he was 12. He studied theatre at Bristol University, where he shared a flat with classmate Sarah Kane, who would be acclaimed as one of the greatest playwrights of her generation following her tragic suicide in 1999.

Following university, Greig was a co-founder, in 1993, of experimental Scottish theatre company Suspect Culture. Established with fellow artists, actor-turned-director Graham Eatough and musician and composer Nick Powell, the Glasgow-based group would champion a modernist, European aesthetic in Scottish theatre for some 16 years.

Throughout his career, the writer and director has displayed an interest in a mind-boggling array of theatre.

Scotland's most prolific, diverse and successful stage writer, his vast output includes the Ibsenesque contemplation of modern Scotland The Architect, the gloriously titled The Cosmonaut's Last Message To The Woman He Once Loved In The Former Soviet Union and Macbeth sequel Dunsinane. Add to that an array of adaptations, ranging from the book for the West End musical of Roald Dahl's Charlie And The Chocolate Factory to Alasdair Gray's magnum opus Lanark, and you get a sense both of Greig's extraordinary fecundity as a writer and his astonishing theatrical range.

Greig, now 47, has always had a profound respect for drama's roots in ancient tragedy – a fact that surfaces in his first Lyceum season, in the shape of the English-language world premiere of The Suppliant Women, by the Ancient Greek dramatist Aeschylus.

Adapted by Greig himself, the almost 2,500-year-old play tells the astonishingly timely tale of a group of Egyptian women who arrive in Athens by boat and seek asylum in the city. Although the piece is the only surviving play of a trilogy, Greig will use the remaining fragments of the other two works and accounts from the time to write a sister drama completing the story.

"The thing about the play that appeals to me deeply is that it's one of the earliest plays, it's the taproot of theatre," he says.

"The Ancient Greeks are enjoying a great moment right now in Scottish theatre," he adds, referring to Chris Hannan's adaptation of Homer's The Iliad, currently being staged at the Lyceum, and Zinnie Harris's This Restless House, her new version of Aeschylus's trilogy The Oresteia, which plays until May 15 at the Citizens Theatre in Glasgow.

This sudden flurry of classicism is not a coincidence, Greig avers. It is, he thinks, a recognition that we are currently living in dramatic and, in terms of the global refugee crises, terrible times.

"We're looking to big questions again. The thing about The Suppliant Women is that it's so now, but it's also completely unencumbered by our preconceptions."

Typically of Greig, this is a very insightful observation. It is easy to categorise contemporary playwrights turning their attention to the subject of migration and asylum as either bleeding-heart liberals or hard-hearted right-wingers.

With Aeschylus, however, the matter of his political agenda doesn't arise. "We don't even know what left-wing and right-wing means [in the context of Ancient Greece]," says the dramatist.

The Suppliant Women is a play which was written, he continues, during, "the foundation of democracy. Aeschylus was creating theatre that was meant to be discussed, because the city itself was in the throes of discovering its form of governance".

Immediately he began working on the play, Greig discovered that its topicality was even more striking than he'd imagined. The opening line of the piece took his breath away, he says. The refugees describe themselves as "women of Egypt, neighbours of Syria, who came here in a boat".

It comes as no surprise that the dramatist has alighted upon an Ancient play with a powerful connection to current events. Greig has always been passionately engaged in matters of national and international politics.

He has long sought to promote discussion and debate through his work. On occasion, he has also taken public stances of his own. Greig, who lives in Fife with his wife and two children, was a committed supporter of the Yes campaign during Scotland's independence referendum in 2014.

Perhaps his most creative intervention in the independence debate was his launching of a lunchtime programme of performances and discussions during the 2014 Edinburgh Festival Fringe entitled All Back To Bowie's. This was named after late rock star David Bowie's famous appeal, "Scotland stay with us", which some wags suggested was actually an invitation to the population of Scotland to visit Bowie's pad in New York.

Given such mercurial activity in the theatre and society, there can be little doubt that Greig will fill the Lyceum with a lust for ideas and a passion for the art of drama. The question is, will his radical vision enable him to fill seats?

If the director is worried on this score, he's not showing it. He is sure, he says, that adventurous, and daring elements of his programming will be embraced by Lyceum audiences old and new.

Like his predecessor, Mark Thomson, Greig thinks those who paint the Lyceum's famous army of season ticket holders as uniformly elderly, well-heeled and conservative are barking up the wrong tree. "We gave a sneak preview of the season to some of our donors," he tells me. "I was thinking, 'how are they going to take this?' They took it very well."

In particular, he remembers a conversation he had with one elderly gentleman. Of the 12 shows on the programme, the two he was most enthusiastic about were The Suppliant Women and The Hour We Knew Nothing Of Each Other. The first play, he knew from his career as a classics professor and the other he saw, directed by famous Swiss stage and film director Luc Bondy, at the Edinburgh International Festival in 1994.

It's another example, says Greig, of why people are wrong to have a stuffy image of the Lyceum audience. "The two most 'out there' shows in the programme were the ones he was welcoming."

His mind has clearly been on higher things, such as Ancient drama and modern humanitarian crises. However the recent resignation of National Theatre of Scotland artistic director Laurie Sansom raises the question, had Greig not just been appointed at the Lyceum, would he have fancied the NTS job?

"No," he says, without equivocation. "The NTS job has got national responsibility. Look at the number of brickbats the artistic director receives, and the stress and strains they have to face. For me it would have been a leap too far."

However, Greig shares the widespread concerns for an organisation that is also losing executive producer Neil Murray and associate director Graham McLaren (who are going to Dublin as joint directors of the Abbey Theatre, Ireland's national drama company). "It's a troubling moment", he comments.

Nevertheless, he continues, the NTS's acclaimed model, as a "theatre without walls", has been a success. "If the [NTS] board take the time to work out precisely what it is that they want, and the management model that they want, I think that whoever takes on that mantle [of artistic director] will have a solid footing."

As for his appointment at the Lyceum, it is, he feels, the right fit, both for him and the theatre. "I've lived in Edinburgh the best part of my life. The Lyceum's like my home theatre.

"It's like if you've been a Celtic fan all your life and you're offered the job as Celtic manager. You're going to do it, aren't you?"

To see full details of the Lyceum's 2016/17 season, visit: lyceum.org.uk