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It is hard to miss. As statement buildings go, this one shouts its cause loudly. Three tiers of seating rise in a high arc, a wide entrance gives onto the dusty arena.
Even seeing it for the first time, I can grasp that this is a stadium of stature – the third largest bullring in the world, where 19,592 souls congregate to watch the blood and bluster of man versus beast.
The Plaza de Toros is Pamplona's heart in more than just a geographical sense.
It is the symbol of a city that is synonymous with bullfighting. Every July (always between July 6 and midnight on July 14), it explodes into the ragged fury of San Fermin, the fiesta that sees Spain's best matadors show off their skills in front of a frenzied crowd.
Six bulls are put to the sword on each of the festival's eight days, and the brave (or foolish) run with these doomed creatures through the city's narrow streets. Television cameras cover this improbable procession, hooves pounding the cobbles, participants falling, horns striking.
It is a brutal event – cruel and completely at odds with modern ideas of animal welfare. But you do not have to be an apologist for bloodsports to appreciate that it is also deeply evocative. Ernest Hemingway captured it superbly in his 1926 book The Sun Also Rises – the story of a group of friends torn apart by lust and drink amid the madness of the fiesta.
In many ways, little has changed in the 86 intervening years.
When I first arrive in the city, I can quickly spot the landmarks that Hemingway made famous: The main Plaza del Castillo, where the group's adventures play out, is still lined with busy bars. Cafe Iruna, the 19th century salon where they recuperate over coffee, is still alive and elegant on the square's northern edge. And Gran Hotel La Perla, the five-star retreat where Hemingway often stayed, still offers the most celebrated view of the bull-run from its rear balconies.
But I am looking for more. It is an early April weekend, and I am hoping to glimpse the Pamplona beyond the bullfight, the city that shimmers for the other 51 weeks of the year.
For Pamplona sings and zings in that way of small Spanish cities. And it existed long before San Fermin. Though now squished into the north-east corner of Spain, it began life as a Roman settlement. From this 75BC start, it grew into the centrepoint of the medieval kingdom of Navarre, whose territory spanned the Pyrenees. Even now, 500 years after Navarre was sucked into Spain (in 1513), Pamplona holds its role as capital of the region.
This rich past is visible in the Catedral de Santa Maria.
Here is a religious house befitting a city of historic significance, big and bulky – though not to everyone's taste. When the French writer Victor Hugo visited Pamplona in 1843, he described it as “the most elegant lady with donkey's ears” – a reference to the twin neoclassical towers that were bolted to the cathedral's 15th century Gothic torso in 1783.
Yet despite this mis-match there is quiet majesty here: in the silent cloisters that linger behind the thick wooden doors; in the tomb of Carlos III, Navarre's greatest king, resident since his death in 1425. Outside, a plaque announces that the cathedral is a stop on the pilgrimage path of the Camino de Santiago.
Just north of the Catedral, the Plaza de Caballo Blanco stares over the top of the city's medieval ramparts – and I'm able to gaze along the line of a three-mile stone barrier that has traditionally given Pamplona shape as much as protection. It was forbidden to build outside the walls until 1915 – a rule that contributed much to the city's cluttered feel, thin streets twisting, churches crammed here and there, structures shoved into unlikely gaps.
But then, Pamplona was always a city ready to defend itself.
Such is clear to the west of the centre, where the Cittadella – a 17th century stronghold of mighty heft – still keeps guard. Nowadays, its once inaccessible interior enjoys retirement as a leafy space, where works by the Basque sculptor Eduardo Chillida nestle among the trees, and children play.
This mix of history and culture continues in the Museo de Navarra, which sits above the start-point of the bull-run on Cuesta de Santo Domingo.
Here, collected artefacts (everything from Roman mosaics and Renaissance murals to slashes of modern art) explain Navarre's back-story – though pride of place goes to an 1804 painting by the Spanish master Goya which swirls with dark signs, the storm clouds gathering behind the figure of 19th century nobleman the Marques De San Adrian suggestive of Napoleon's coming threat to Spain.
Of course, there is more to the city than these expired centuries. On a warm Saturday morning I head into the Ensanche district – the area that has spilled south of the bullring since the ban on construction outside the walls was lifted.
Here is modern Pamplona in weekend mode, perusing the shops on the arrow-straight Avenida de Carlos III or seeking fresh fruit and syrupy olive oils in the Mercado del Ensanche. There is a hum of old Spain to this covered market, elderly matriarchs checking lemons for ripeness – but also a hipness in the attached El Mercado restaurant, where light filters through an army of wine bottles stacked against the windows, and merluza (hake) tacos with red peppers cost €14.
In fact, there is a pronounced hipness to the city's food scene: in the cool confines of Rodero, a 37-year-old family eatery that has blossomed into a Michelin-starred restaurant (where a spicy beef tartare with truffles is €25); in the similarly swish Enekorri, which looks like a cutting-edge furniture showroom as much as a culinary enclave, and does an excellent salted octopus with rice for €22; among the busy tables of Bar Gaucho, a pintxo (tapas) bar near the bullring, where bite-sized morsels such as ajoarriero (a pastry parcel of flaky cod and poached egg) and anchovy tostadas with a gazpacho chaser come rather cheaper (€3 and €2.80 respectively) – but are no less delicious.
I have Saturday lunch here, stacking up plates under walls bearing photos of matadors, other diners idling at the bar, discarded napkins piling up on the floor, a buzz of lively chatter hanging on the air.
This brings me full circle to the Pamplona of bullfights and bravado.
But before I leave, I make one last call, at an outpost far removed from this classic image of the city – though just three miles away in the hamlet of Alzuza. Here, the urban edges of Pamplona already surrendering to the fields of rural Navarre, the Museo Oteiza crowns a hilltop.
The former home of the Basque sculptor Jorge Oteiza, it now hosts his life's work – a glut of angular creations cocooned in a gallery of concrete and glass. Some of the pieces are hard and impenetrable, but there is warmth too, windows peering onto the pastoral scene outside.
As my Sunday afternoon ebbs away, the museum feels like a discovery. But then, Pamplona is a city that, beyond the din and dust of San Fermin, is well worth unearthing.
Iberia (0870 609 0500; www.iberia.com) flies to Pamplona daily from Heathrow via Madrid or Barcelona, from £250. Double rooms at the Gran Hotel La Perla (www.granhotellaperla.com) start at £153 – and from £132 at the Hotel Alma Muga de Beloso (www.almapamplona.com).