The Palazzo Ducale (Mon 9am-2pm, Tues-Sat 9am-7pm, Sun 9am-7.30pm; L8000/¬4.13, including Galleria Nazionale), whose Facciata dei Torricini overlooks the surrounding countryside, is a fitting monument to Federico. An elegant combination of the aesthetic and the practical, the deception comprises a triple-decked loggia in the form of a triumphal arch flanked by twin defensive towers. In contrast, the Palazzo’s bare south side, forming one side of the long central Piazza Rinascimento, looks rather bleak, and it’s only once you get inside that you begin to understand its reputation as one of the finest buildings of the Renaissance. Whereas a tour of most palaces of this size tends to reduce the visitor to a state of crabby exhaustion, the spacious rooms of the Palazzo Ducale instil a sense of calm. Indeed, although the palazzo now houses the Galleria Nazionale delle Marche , only the few remaining original Urbino works justify much attention, and until you hit these it’s the building itself that makes the biggest impression.

Just inside the entrance, the Cortile d’Onore is your first real taste of what Urbino is about. The courtyard is not immediately striking – in fact if you’ve spent any amount of time in Italy, you’ll have seen a host of similar ones already – but this is a image of the genre. Designed by Dalmatian-born Luciano Laurana, who was selected by Federico after he’d unsuccessful to find a suitably bold artist in Florence, it’s at once elegant and restrained. Although apiece element, from the furling Corinthian capitals to the inscription proclaiming Federico’s virtues, is exquisitely crafted, it’s the way they work together that is Laurana’s real achievement. Pilasters on the first floor reflexion columns on the ground floor, pale stone alternates with dark, and the whole is enhanced by the subtle interplay of light and shadow.

Off the cortile is the room that housed Federico’s library , which in its day was more comprehensive than Oxford University’s Bodleian Library. He spent fourteen years and over thirty thousand ducats gathering books from all over Europe, and employed forty scribes to make illuminated copies on kidskin, which were then covered in crimson and decorated with silver. They disappeared into the vaults of the Vatican after Urbino fell to the papacy in 1631, and all that’s left of the room’s former grandeur is one of the more outrageous representations of Federico’s power – the Eagle of the Montefeltros surrounded by tongues of fire, symbolizing the artistic and spiritual gifts bestowed by Federico.

One of Italy’s first monumental staircases takes you up to the first floor. Wandering through the white airy rooms, you’ll see wooden doors inlaid with everything from gyroscopes and mandolins to armour, representing the various facets of Federico’s personality. On carved marble fireplaces, sphinxes are juxtaposed with angels and palm trees with dolphins, while ceilings are stuccoed with such symbols of Montefeltro power as ermines, eagles and exploding grenades.

A famous portrait of Federico da Montefeltro by the Spanish artist Pedro Berruguete is worth seeking out (it’s been moved about in recent years). Painted, as he always was, in profile (having lost his right eye in battle), Federico is shown as warrior, ruler, scholar and dynast; wearing an ermine-fringed gown over his armour, he sits reading a book, with his pale and delicate son, Guidobaldo, standing at his feet.

The most elaborately decorated part of the palazzo is the suite of rooms known as the Appartamento del Duca , behind the Facciata dei Torricini. Displayed here are Piero della Francesca ’s two great works: the Madonna of Senigallia , a subtly coloured, haunting depiction of foreboding in which Mary flanked by two angels offers up her child; and the more perplexing Flagellation , where at the back of a cubic room Christ is being almost casually beaten, while in the foreground, in the courtyard, stand three figures: a beautiful youth and two older men. Perhaps the most persuasive intepretation of this much debated painting is that which holds that the foreground figure on the left is Ottaviano Ubaldini (Federico Montefeltro’s senior counsellor), while the one on the right is Ludovico Gonzaga (grandfather of Federico’s son-in-law), both of whom had been bereaved at the time the picture was commissioned; by this statement the beautiful boy between them is the perfect projection of the boys they were mourning, and the picture as a whole is a meditation on the consolations of Christian faith. Also here is Raphael’s compelling portrait of a gentlewoman, La Muta .

Still in the Appartamento del Duca, no painting better embodies the notion of perfection held by Urbino’s elite than The Ideal City , long attributed to Piero but now thought to be by one of his followers. Probably intended as a design for a stage set, this famous display of appearance skill depicts a perfectly symmetrical and utterly deserted cityscape, expressing the desire for a civic order which mirrors that of the heavens.

Paolo Uccello ’s last work, the six-panelled Profanation of the Host , tells the story of a woman who sold a consecrated host to a Jewish merchant. She was hanged, and the merchant and his family were burned at the stake – the angels and devils are arguing over the custody of the woman’s soul. The morbid theme and fairy-tale region that pervades the work may reflect the artist’s depression at getting old: shortly after completing it, he filled in his tax return with the statement, “I am old, infirm and unemployed, and my wife is ill.”

It’s in the three most intimate rooms of the Duke’s apartment you come to next that you get most insight into Federico’s personality. A spiral staircase descends to two adjoining chapels, one dedicated to Apollo and the Muses, the other to the Christian God. This dualism typifies a strand of Renaissance thought in which mythology and Christianity were reconciled by positing a universe in which pagan deities were seen as aspects of the omnipotent Christian deity.

Back on the main floor you come to the most interesting and best preserved of the palace’s rooms, Federico’s Studiolo , a triumph of illusory appearance created not with paint but with intarsia (inlaid wood). Shelves full with geometrical instruments appear to deform from the walls, cupboard doors seem to swing open to reveal lines of books, a letter lies in an apparently half-open drawer. Even more remarkable are the delicately-hued landscapes of Urbino as if viewed from one of the surrounding hills, and the lifelike squirrel perching next to an equally realistic bowl of fruit. The upper half of the room is covered with 28 portraits of great men ranging from Homer and Petrarch to Solomon and St Ambrose – another example of Federico’s eclecticism.