The event, which this year celebrates its 50th birthday, is the biggest arts festival in the world. With its hundreds of fringe performances, it burrows into every nook and cranny of the city. Many of the performances take place within easy reach of the High Street, the historic backbone of the city, stretching the Royal Mile down from the castle to Holyrood Palace.
We start half a mile or so to the west of the High Street - at the Usher Hall on Lothian Road, where the festival started in 1947. The Usher Hall will also host this year's opening concert, on Sunday August 10. In some ways similar to, but much smaller than, London's Albert Hall, it is a memorial not to royalty but to beer, which remains a staple Edinburgh industry.
Next to the Usher Hall is the Traverse Theatre, which presents new drama all year round. And on the other corner, in Grindlay Street, is the Lyceum, home of the city's rep company. We walk past the Lyceum to join Johnston Terrace, which takes us up to the Old Town, flanking the south, or backside, of the castle, the side nobody photographs.
Where the road joins the Royal Mile stands the Highland Tolbooth Church, earmarked with Lottery money to become the festival headquarters. You could turn left to the castle, but our route is east and downhill. First pause at the back of the Assembly Hall, home to the national Church's annual gathering. It was here that the festival had its first great Scottish triumph, Tyrone Guthrie's production of The Three Estaits, a pre-Reformation satire on the sleaze of the day. I am too young to remember its 1948 production but it has been revived since, always in the remarkably uncomfortable Assembly Hall, and always a reminder that Scotland has a distinctive dramatic tradition.
Some festivals ago I went to a long Austrian play at the hall. There were several intervals and adjourning to the Jolly Judge, a pub in James' Court (highly commended), we skipped a whole act, the only one, as it turned out, containing any debauchery.
At St Giles Cathedral my predecessor as editor of The TES Scotland, Colin Maclean, put on an opera - of which he wrote the libretto - about Hugh Miller, the Victorian geologist. Behind the cathedral are law buildings including the Signet Library, which has one of the most handsome rooms in Scotland. It was used for a revival of John Home's play Douglas, which was not very good, and created a scandal when presented to Calvinist Edinburgh in 1756. Its supporters were roused to patriotic but misplaced shouts of "Whaur's yer Wullie Shakespeare noo?" Our walk continues across the bridges and past John Knox's house (it probably wasn't his at all) to the Netherbow Theatre, a friendly place associated with the Church of Scotland. A little further downhill is the old boundary of Edinburgh. The rest of the Royal Mile was in the separate burgh of the Canongate.
Old Playhouse Close is nearby, home of early (immoral) theatre. The closes (or lanes) off the Royal Mile should be explored for their individuality and atmosphere. You feel you might run into David Hume or Boswell, but Old Playhouse Close has, for some reason, a locked gate.
A hundred or two yards on, you come to Moray House Institute, which produces teachers and has a theatre where I once performed without distinction. I was an 18-year-old schoolboy trying to be a middle-aged doctor, fortunately not for a festival fringe audience.
Near the bottom of the hill is Lochend Close, through which one reaches the hideous Harry Younger Hall. I mention the hall only because I saw a rather good fringe production of Schiller's Maria Stuart there. But don't linger. Have a drink in Jenny Ha's next door, which John Gay of The Beggar's Opera visited more than 200 years before the annual pilgrimage of today's luvvies. Or complete the walk at Holyrood, where the real Mary Stuart created her own dramas - fancy-man Rizzio murdered in the palace, husband Darnley done in at the nearby Pleasance.
Walks in Edinburgh's Old Town by Michael and Elspeth Wills, published by Mercat Press at Pounds 5.99, explores the territory more fully