When the bull of foundation arrived in 1413, sent by Pope Benedict XIII, the small huddle of clerics and scholars who had been teaching unofficially in St Andrews finally had a university. It was the first in Scotland and the third in the English-speaking world, beaten only by Oxford and Cambridge. The town then was already a place of pilgrimage, drawn by the relics of Saint Andrew kept in its now-ruined cathedral. The university grew up around that sanctity. St Salvator's College was founded in 1450, St Leonard's in 1512, and St Mary's in 1538. The Chapel of St Leonard's holds stones dating from 1144, older than the university itself. Walking from one quad to the next, you pass through centuries the way other places pass through neighbourhoods.

Set into the cobbles outside the main gate of St Salvator's, the initials "PH" mark the place where Patrick Hamilton was burned at the stake in 1528. Hamilton was twenty-four, a young Protestant theologian whose death helped spark the Scottish Reformation. Six centuries later, students still go out of their way to avoid stepping on those letters. Tradition holds that anyone who treads on them will fail their degree. There is a remedy, and it is exactly as Scottish as you might hope: on May Day at dawn, students gather and run together into the freezing North Sea, washing away academic sin while the University Madrigal Group sings on the sand. They call it the May Dip. They also call it, more practically, a reason to swim before exams.

In September 2001, a new geography student named William moved into St Salvator's Hall. He met a fellow student named Catherine Middleton at breakfast on the first day. They became friends, then flatmates with two others on Hope Street, then a couple. They graduated together in 2005, William with a degree in Geography, Catherine in History of Art. Nine years later, as Prince William and Princess Catherine, they returned to receive honorary degrees. The locals took it in stride. St Andrews has watched royalty come and go for longer than most countries have existed. Long before William and Catherine, King James II of Scotland studied here, and James I of England (then James VI of Scotland) founded the university library in 1612 with a personal donation of three hundred and fifty books.

Each new student, called a Bejant if male or Bejantine if female, is assigned academic parents - third- or fourth-year students who guide them through the strange weather of first year. The reward, by tradition, was a pound of raisins. The reward, by modern practice, is a bottle of wine. In return the parents write their academic children an elaborate receipt, in Latin, on whatever surface they choose - a surfboard, a fish, a refrigerator. On Raisin Monday, every first-year gathers at noon outside St Salvator's clutching their receipts, ready to be challenged on the accuracy of their Latin by older students. Errors are inevitable. The whole ceremony now ends in a shaving-foam fight on the Lower College Lawn. The university provides a special first-aid hotline for the weekend.

The town sits on a headland where Fife ends and the North Sea takes over, just south of the wide blue mouth of the Firth of Tay. RAF Leuchars airfield, now a British Army base, lies a few miles to the northwest, its runways once shielding St Andrews from German bombers. Dundee Airport is just across the Tay estuary. The University Library on North Street holds over a million volumes, including the King James Library from 1643. The Bell Pettigrew Museum keeps the bones of a dodo and a Tasmanian tiger, animals as extinct as the certainties of the world that built these colleges. Notable alumni run from John Knox to John Napier to Tolkien lecturer J. R. R. Tolkien himself, who delivered his famous "On Fairy-Stories" address here in 1939. Six hundred years of names, and counting.