On a gently sloping hill overlooking the north-Italian town of Vicenza is the most perfect building designed by the most influential architect of Western civilisation: Andrea Palladio, born in 1508. The Villa Almerico Capra Valmarana, known as La Rotonda, resembles a temple, with its portico of Ionic columns and dome, which is appropriate since Palladio designed it for a canon retiring from the papal court.
La Rotonda is the most visited of Palladio's 19 surviving villas, which dot the countryside around Vicenza and the neighbouring provinces. Together with the old town – which has most of Palladio's civic work – they form a Unesco World Heritage Site. Vicenza's pedestrianised streets are the best place to see how the ideas of this stonemason from Padua were translated into buildings across Europe, Russia and the States. The legacy of his influence in such buildings as the White House in Washington DC was largely due to the cultural journeys made by Englishmen to Vicenza and the Vicentine.
Palladio would probably have remained a stonemason had it not been for Count Gian Giorgio Trissino, whose portrait hangs in the Louvre. Palladio had the good luck to be involved in remodelling Trissino's home, Villa Trissino Trettenero, on the northern edge of Vicenza. It was the first in Vicenza composed in the classical style of the Roman Renaissance. Trissino became Palladio's patron and mentor, taking him to Rome and introducing him to future clients, as well as offering Palladio the chance to study the classical buildings.
These experiences helped Palladio to gain his first public commission, a remodelling of the Early Renaissance Palazzo della Ragione on the Market Square, where Vicenza's council once met. With consummately bad timing, given the 500th anniversary of Palladio's birth now being celebrated in the town, it is currently being restored, but sections of the screen with which the architect surrounded the building can be seen between the scaffolding. The practicality of the design, creating covered space for people to walk past the shops, is typical of Palladio's approach (as clearly expressed in his The Four Books of Architecture).
But the building everyone visiting Vicenza feels they must see is the Teatro Olimpico on Piazza Matteotti. It is the only surviving Renaissance theatre with original backdrop of streets in a receding perspective radiating off the stage. Palladio applied his knowledge of ancient Roman theatres to the building and its semicircular auditorium. As with other buildings unfinished at Palladio's death in 1580, it was completed by the envious architect Vincenzo Scamozzi, who sold some of the older man's drawings to Inigo Jones when he came to Vicenza in 1613 to study Palladio's work.
Leaving the theatre precincts, you look across the street to Palladio's Palazzo Chiericati, with its dramatic double colonnade. Oddly, it's reminiscent of West Wycombe Park in Buckinghamshire, almost certainly inspired by Palladio's urban villa of 1550. The palazzo became the town museum in 1855, but the most extraordinary adaptation of a palazzo is to be found at Palazzo Thiene on Contra Porti 12. Built between 1542 and 1560, the Thiene family home was bought by the Banca Popolare di Vicenza in 1872. Though part of the building is now offices, the principal frescoed rooms can be visited, and the attic and cellar spaces have been imaginatively adapted into an art gallery and coin museum.
The best place to appreciate the beauty and practicality of Palladio's work lies at the northern edge of the Veneto plain, where the ground begins its gradual ascent to the Alps. To the east of Asolo, a jewel of a small town where the explorer Freya Stark had a house, lies Villa Barbaro di Maser, the most handsomely decorated villa in north Italy, with the largest set of frescoes by Veronese. It was built in the late 1550s for two brothers who, though Venetian aristocrats, were dependent on the surrounding farm for their affluent lifestyle.
The perfectly symmetrical pale yellow house was recently inherited by Diamante Buschetti, whose grand-father bought it in 1934 and whose mother continued its restoration. But the most remarkable thing is that it is the only Palladio villa still being run as an agricultural estate. You look out from the balcony on the central block over vineyards producing grapes for an award-winning chardonnay. The axis of the gently sloping drive is a fountain and semi-circle where Palladio wanted carriages to pause while their occupants admired his work and horses were watered. Beyond, an avenue of trees leads the eye across the plain. The estate also produces olive oil and wheat. It is a measure of Palladio's concern for practical details that the water from the fountain was channelled into the kitchen for washing, thence to the garden for irrigation.
It was from Villa Barbaro that Lord Burlington bought his first Palladio drawings when he visited in 1719, later using them to illustrate publications that disseminated Palladio's ideas. As the builder of one of the nearest houses in Britain to a Palladian villa – Chiswick House in London – Lord Burlington also bought Inigo Jones's collection of Palladio drawings, the majority now held by the Royal Institute of British Architects.
Closer to Vicenza stands Palladio's most strikingly situated villa, also his first complete building, the Villa Godi, which he began in the late 1530s. It stands on a spur above the village of Lonedo, and is an austere building until one ascends the steps to the arcaded loggia and enters a sequence of nine frescoed rooms. The family lived in these, with kitchens and cellars below, granaries above, the normal arrangement of a Palladian country villa. During the First World War, it became the HQ of English troops battling for the Asiago Plateau.
To the south-east of Villa Godi lies Villa Emo. After 440 years in the same family, it was too hard to maintain and was bought by a bank, which has kept it open for visitors. Avenues of poplars stretch away on both sides of the loggia; the interior is a riot of colour, with frescoes by Giambattista Zelotti on martial, mythological and allegorical themes.
Palladio's influence owes much to Inigo Jones and Lord Burlington, but credit for launching the Palladian movement must also go to Giacomo Leoni. This Venetian architect translated The Four Books of Architecture into English and designed Lyme Park in Cheshire (Mr Darcy's home in the BBC's Pride and Prejudice) and Clandon Park in Surrey.
Although it was the printed page that launched Palladianism, Goethe insisted it was no substitute for the real thing: "No reproductions of Palladio's designs give an adequate idea of the harmony of their dimensions... You have to see these buildings with your own eyes to realise how good they are."
Sleeper trains from Paris Gare de Bercy stop at Vicenza; returns from London start at £119 with Rail Europe (0844 848 4070; www.raileurope.co.uk). BA (0844 493 0787; www.ba.com) flies to Verona from Gatwick.
Hotel Campo Marzio, Vicenza (00 39 04 44 545 700; www.hotelcampomarzio. com). B&B from €140 (£117).
Albergo Al Sole, Asola (00 39 04 23 951 332; ww.albergoalsole.com). B&B from €145 (£121)
The Landmark Trust (01628 825925; www.landmarktrust.org.uk) rents out the Villa Saraceno from £307 per night.
"A Walk with Palladio" guided tours of Vicenza depart Saturday afternoons until 1 November; coach tours depart Sundays until 2 November (00 39 04 44 320 854; www.palladio2008.info).
The exhibition "Palladio 500 Years" opens today at Palazzo Barbaran da Porto, Vicenza (00 39 02 433 535 22; www.palladio500anni.it), to 6 January. Open Sun-Thurs 9.30am–7pm, until 9pm Fri and Sat; €10 (£8.30).
Teatro Olimpico (00 39 04 44 222 800; www.museicivicivicenza.it). Villa Barbaro di Maser (00 39 04 23 923 004; www.villadimaser.it). Villa Godi (00 39 04 45 860 561; www.villagodi.com)Villa Emo (00 39 423 476334).
Trattoria Molin Vecio, Caldogno (00 39 444 585168; www. molinvechio.it). The restaurant has devised a €25 (£21) menu using home-grown ingredients that would have been popular in Palladio's day.
Vicenza tourist office: 00 39 04 44 994 770; www.vicenzae.org