Hemmed in by walls on three sides and a brackish loch on the fourth, the medieval Old Town could not spread outward, so it grew upward. Tenements stacked to twelve and fourteen storeys - the first urban high-rises in Europe. Multiple families shared a single stairway, called a close, descending steeply on either side of the High Street like fishbones. Some 80 closes still exist; each was named for a famous resident or trade. The chamber pots emptied into the open drain down the middle of the cobbles, accompanied by the shouted warning 'gardyloo' - from the French gardez l'eau, mind the water. The smoke from ten thousand coal fires hung over everything. From the hills of Fife across the firth, the city smelled before it could be seen, and the nickname Auld Reekie - Old Smoky - has stuck for four hundred years.

The Mile begins at the Castle Esplanade, where the Royal Edinburgh Military Tattoo plays out every August. Just below stands the Tolbooth Kirk - now called The Hub - a confident Victorian Gothic church never consecrated, its spire the highest point in the central city outside the castle. Halfway down, opposite St Giles' Cathedral, a brass mosaic in the pavement marks the Heart of Midlothian: the site of the former Tolbooth, council chamber and jail and place of public execution until 1817. Walter Scott bought the old iron door when the building came down and kept it. It is customary to spit on the mosaic for luck. In the 1870s a group of lads were chased off these cobbles by a policeman; they founded a football club they named Heart of Midlothian. Down below the High Street the road becomes Canongate, governed historically by the canons of Holyrood Abbey - a separate burgh beyond the city's reach, ideal if you needed to dodge the city bailiffs.

South of the castle the medieval city overflowed in the 14th century into the dank hollow of the Grassmarket, where livestock were traded and condemned criminals were hanged. By the 18th century the area was tenement housing for the poor and the desperate. In 1828 the West Port at its western end became the address of William Burke and William Hare. They preyed on lodgers and strangers, plied them with drink, suffocated them - the technique still called 'Burking' in textbooks of forensic medicine - and sold the fresh bodies to Dr Robert Knox, a leading anatomy lecturer at the university. Knox paid handsomely and asked no questions, preferring fresh corpses to the pungent goods of grave robbers. Sixteen people died before the killers were caught. Hare informed on Burke and walked free; Burke was hanged in 1829, and Knox's career was destroyed even though he was never charged.

Greyfriars Kirkyard, behind the market, is full of melancholy 17th-century tombs and the bones of plague victims. Outside its gates stands a Victorian drinking fountain topped with the small bronze statue tourists endlessly photograph. Greyfriars Bobby was a small terrier owned by John Gray, a nightwatchman. When Gray died in 1858 Bobby refused to leave his master's grave, and was fed by neighbouring innkeepers for fourteen years until his own death in 1872. The statue was erected the following year. It depicts a Skye terrier. Surviving photographs of the actual Bobby show a Dandie Dinmont - a different breed entirely. The story endures regardless. The author J. K. Rowling, who wrote much of Harry Potter in a cafe nearby, lifted several names from the gravestones in the kirkyard, including Thomas Riddell and William McGonagall.

South and east of Holyrood Palace lies Holyrood Park, created by King James V in the 16th century as royal hunting ground and a wilderness in miniature inside the city walls. It is dominated by Arthur's Seat, the main vent of a volcano that erupted 340 million years ago in the Carboniferous Period. Its summit reaches 251 metres (823 feet); the easiest ascent takes about ten minutes from Dunsapie Loch car park on the east, but most walkers come from the west, scrambling up a steep gully called the Gutted Haddie. The Salisbury Crags - a curtain of basalt cliffs facing the city - became the laboratory where the 18th-century farmer and geologist James Hutton found the field evidence for his theory of deep time, proving the Earth was vastly older than scripture allowed. Hutton's section, where igneous rock intruded into older sandstone, is still there in the cliff face.