Spoleto is justifiably proud of its Latin title, Caput Umbriae (“Head of Umbria”). Once upon a time it really was one of the most important cities in central Italy, commanding an extensive territorial allegiance.

Piazza del Duomo is an open space cleared during the last fifty years, between the sloping Via dell’Arringo (another version of the English and French ‘harangue’) and the façade of the cathedral of Santa Maria Assunta, which echoes on summer nights to the voices of playing children. As the inscription tells us on the mosaic of Christ blessing the Virgin and St. John adorning the upper level of the façade, “Solsternus, greatest of living masters in this art, made this in the years which you will find out by adding one thousand and seven to two hundred”. The portico, fusing grey with pinkish stone, was completed in 1504, but the original Romanesque doorway survives below, though only one of the customary couchant lions supports a flanking pillar.

Surprisingly, the interior is a majestic baroque basilica, the work of Luigi Arrigucci, a Florentine architect who began its reconstruction in 1638. An earlier building had been systematically pillaged by Fulvio Orsini, bishop from 1562-81. His successor Maffeo Barberini took Spoleto to his heart, and when a nephew, Francesco, became Pope Urban VIII in 1623, plans were initiated for restoration. Arrigucci was Urban’s court architect and, whatever the hostile criticism of the greedy, ambitious Barberini family in Rome, nobody could deny the splendour and lavishness of their patronage of the arts. Appropriately, though you cannot see it very well, the bust of Urban high above the main entrance is by that most famous of all his protégés, the sculptor Gian Lorenzo Bernini.

To your right, the chapel of Bishop Costantino Eroli has an apse and vaulting decorated in 1497 by Pinturicchio, and though the frescoed Madonna with Saints in a romantically envisaged landscape is much damaged, the painter’s grace and tenderness shine through. Who created the enthralling mixture of biblical themes, motifs from pagan mythology and symbolic elements in nearby Cappella dell’Assunta is not known for certain, but it was probably the Palermitan painter Jacopo Siculo (1508-44).

In the north transept you will find the tomb of the great Florentine artist Filippo Lippi (1406-69). He may not have been the most exemplary of personalities, but he was certainly most engaging, as Robert Browning clearly felt when in 1853 he wrote his Fra Lippo Lippi, a dramatic monologue in which the painter divulges his artistic credo. An unwilling Carmelite monk, Lippi had trouble controlling his “animal lusts”, as Vasari tells us, and escaped from a room in which Cosimo de’ Medici had locked him (so as to get a picture finished) by knotting his bed sheets together. Invited to Spoleto with his pupil Fra Diamante to decorate the cathedral apse, he is said to have been poisoned by relatives of a woman with whom he was conducting an affair. When the Spoletans asked Lorenzo de’ Medici whether they might keep his body, as their city lacked “the ornament of eminent persons”, that great-hearted Florentine paid for a tomb to be placed here, designed by Lippi’s bastard son Filippino (1457-1504), and commissioned a Latin epitaph by the poet Angelo Poliziano.

The apse frescoes themselves, recently restored, were begun in 1467. celebrating the Blessed Virgin’s life, with scenes of the Annunciation, Nativity, Dormition and Coronation, they underline Filippo Lippi’s irrepressible liveliness and humanity. Note, for example, Mary’s demure confusion, expressed by her downward-tilting head and awkwardly turned hands as Gabriel greets her, or the throng of rejoicing angels which offers lilies to the kneeling Madonna.

The original open space at the heart of Spoletium must have been much larger, but the Piazza del Mercato is still the core of the city, the very archetype of an Italian town square, with its restaurants, cafés and vegetable market and a grandiose fountain at the north end, designed in 1746 by the Roman architect Costantino Fiaschetti.

Beyond, from the tree-shaded Piazza Campello, you can climb up to the massive Rocca Albornoz, one of the key fortresses of the Papal States. Built by Cardinal Albornoz in the fourteenth century and in use until recently as a penitentiary, it is now being turned into a cultural centre for the city. Out from its eastern ramparts, your view over to the slopes of Monteluco takes in a handful of medieval dovecots among the trees. Once there were many more of these dotting the landscape, and their builders were summoned much further afield than Italy, for you can find similar pigeon-lofts in the Greek islands, made by Umbrian masons for the Venetians and Genoese.

Travellers have always admired the colossal lime-stone aqueduct spanning the valley, known as the Ponte delle Torri and designed during the fourteenth century, probably by the Gubbian architect Gattapone, working to a commission from Cardinal Albornoz. Crossing this (it can still, if necessary, be used to carry water to the city), you find yourself on the hillside of Monteluco, where a dense forest (lucus is the Latin word for grove) preserves the atmosphere which encouraged St Isaac and his Syriac anchorites to establish their cells here. The hermitages remained independent of monastic rule until Napoleonic times, and though they are now private dwellings, you can occasionally get a glimpse of the Eremo delle Grazie, substantially restored in 1727, together with its little church, by Cardinal Camillo Cybo, assisted by an anonymous architect.

North-west of Monteluco, above the noisy Via Flaminia, the church of San Pietro offers a final Romanesque flourish. It was founded around AD 600 on the site of an Iron Age necropolis by Bishop Achilleus, who had brought from Rome one of the chains which held St Peter in prison. The sculptor of the remarkable sequence of romanesque panels of the façade is unknown, but their arrangement is as singular as their workmanship. No merely decorative idea lies behind the presence of a ploughman with his team, a deer suckling her fawn, or a Aesopian scenes of wily foxes and wolves. Each is carefully linked with a symbolic scheme of human redemption through faith and good works, and the Spoletans thought so highly of the whole façade that they left it alone when the interior of the church was rebuilt in frigid baroque idiom in 1699.