Leiden grew up where the Oude Rijn and the Nieuwe Rijn meet, around an artificial hill called the Burcht that was probably first raised as a refuge from floodwater. By the 11th century there was a small wooden fortress on top of it. In the centuries that followed the village around the mound thickened into a town, then a textile city. By the late 15th century Leiden was one of the biggest broadcloth producers in northern Europe, with weavers' workshops crowded along the canals. The river-bound geography that had once protected the Burcht now organized everyday life. Quays, drawbridges, and warehouses replaced reed beds. The two arms of the Rhine still slip through the centre of town, lined with townhouses whose front doors open almost straight onto the water.

When the city sided with the Dutch Revolt in 1572, Spain answered. The 1574 siege lasted from May to October, and as silver ran out the city stamped its own emergency currency on paper torn from prayer books, one of the earliest uses of paper money in Europe. By the time William's ships came in across the flooded polders, around five thousand of the city's roughly fifteen thousand residents were dead. Every 3 October the city still marks the relief with parades, historical reenactments, a funfair, and hutspot, the carrot-and-onion stew said to have been left bubbling by retreating Spanish soldiers and eaten by the starving defenders. It is not a quiet anniversary. Children run loose. Bands play under the windows of houses that were standing during the siege itself.

Because Leiden's economy slumped from the late 17th century until the middle of the 19th, the city was too poor to tear itself down and start over. The accident of decline preserved one of the largest 17th-century town centres in the Netherlands, second only to Amsterdam. Walk the Rapenburg today and you are walking past the canalside facades that Rembrandt, who was born here in 1606 and trained as a painter here, would still recognize. Lucas van Leyden, Jan van Goyen, and Jan Steen all worked in this same compact grid of canals. A century-old wall-poems project has painted more than a hundred of those facades with poetry in dozens of languages, so that turning a corner can put a stanza of Rilke or Lorca above a parked bicycle.

On 12 January 1807, a boat carrying around eighteen thousand kilograms of gunpowder exploded in the middle of the city. One hundred and fifty-one people were killed, more than two thousand injured, and roughly two hundred and twenty homes destroyed. King Louis Bonaparte, brother of Napoleon, came personally to organize relief. The crater the blast left in the centre of Leiden stayed empty for nearly eighty years. In 1886 it was turned into the Van der Werff park, named for the mayor who had refused to surrender during the 1574 siege. Two civic traumas, separated by two and a half centuries, sit in the same patch of grass.

Leiden calls itself the City of Discoveries, and the claim is not just civic boosterism. Snell's law was worked out here. The Leyden jar, the first practical capacitor, was invented in 1746 by Pieter van Musschenbroek in his laboratory in town. In 1908 Heike Kamerlingh Onnes liquefied helium for the first time in a Leiden cellar and then pushed temperatures to within one degree of absolute zero, where he discovered superconductivity. Einstein lectured here. The Hortus Botanicus, planted in 1590, is among the oldest botanical gardens in the world, and tulip bulbs cultivated within its walls helped seed the Dutch tulip trade. Modern Leiden is still a university town first, with about thirty-five thousand students walking the same streets the Pilgrims walked before they sailed to Plymouth. The city hosts the Leiden International Film Festival, the European headquarters of Eurotransplant, and the Airbus group office, but its real export remains what it has been since 1575: educated people.