If you want to understand modern Iran, the British Museum asserts, the best way is to start with the reign of Shah Abbas I. He came to the throne in 1587, the fifth ruler of the Safavid dynasty, and is remembered as one of the country’s most influential kings. The British Museum’s exhibition Shah Abbas: The Remaking of Iran is timely, therefore, given that Iran recently marked the anniversary of the 1979 revolution that put an end to the rule of the Shahs.

The exhibition, the third in their series about great rulers following on from the first emperor of China and the Roman emperor Hadrian (next in line is Moctezuma), is again in the Reading Room. I’d thought, maybe you too, that the Reading Room was to be used only for the China and Hadrian exhibitions, but now know that the original planning permission has been extended to allow for major exhibitions until 2012. I’m also told that all’s well beneath the Reading Room, the desks and so on are checked regularly.

The reign of Shah Abbas (1587-1629) brought a much needed stability to his country following years of invasion and internal conflict; he re-conquered lost territories, strengthened the economy and transformed his realm into a centre of international trade and cultural exchange.

A map at the start of the exhibition highlights Persia’s (as Iran was then called) strategic position and historical context: Shah Abbas ruled a country centrally placed between Elizabeth I’s England, Phillip II’s Spain, Emperor Akbar’s Mughal India, the Ottoman Empire of Sultan Murad II, and Ming dynasty China.

It focuses on four key sites that Shah Abbas transformed or lavishly donated to as public statements of royal power and piety: Isfahan, the magnificent new capital created as a showcase for his reign, and three major Shi’i shrine cities — Mashhad, Ardabil and Qum. Objects from these places, many of them not seen before outside Iran, include magnificent Qur’ans, mosque lamps, paintings, calligraphy, Chinese porcelains, metalwork and luxurious gold-ground carpets and silks.

Having said that, I was disappointed to see only a few tiles here; instead, there’s a large rolling show at the heart of the exhibition highlighting the breathtaking beauty of those fabulous buildings, their walls covered every inch with exquisite tiles. Here you can sit back beneath the dome of the Reading Room and gaze up at projected views melding one into the other: the mosques, the ceilings, the mesmerising patterns, colours, inscriptions and arabesques, the slanting latticework shadows. And if you hit a certain button on the audio guide, you can enjoy some Iranian music, too.

There are few pictures of the Shah because of the Islamic ruling against the human image. One here, however, a small watercolour from 1618, when he was at the peak of his powers, shows a slender man with distinctive drooping moustaches, a sharp nose, and keen eyes. He was a “restless, decisive, ruthless and intelligent” ruler explains exhibition curator Sheila Canby.

“Religion was central to the reign of Shah Abbas,” says museum director Neil MacGregor. “He presented to his people the image of a deeply pious figure.”

And although Shi’ism was made the state religion by his grandfather in 1501, it was Shah Abbas who linked his nation’s identity with it, the same way as Elizabeth I linked England with the Protestant faith.

He demonstrated his personal piety in many ways: he made a 600-mile pilgrimage on foot to Mashhad, the holiest site in Iran, the burial site of Imam Riza, the only Shi`’i imam buried in Iran; he also donated scores of precious objects to shrines. There are some beautiful examples here, Chinese porcelains, mosque lamps and manuscripts from Ardabil, for instance, a shrine he renovated in north-west Iran containing the tomb of Shaykh Safi, a fourteenth-century sufi mystic and ancestor of Shah Abbas. He made a ‘China House’ there out of a tomb chamber to display his donations.

Two pieces from Ardabil stood out for me: a large bulbous porcelain flask from China covered in graceful blue waves (Ming dynasty c.1403-35); and further along the row, a large, early 14th-century dish decorated with a white, three-clawed dragon chasing a flaming ball on a deep cobalt blue ground. White decoration on a blue background is apparently very unusual and technically extremely difficult. It certainly was very striking.

“It was a golden age for the arts in Iran,” exhibition curator Sheila Canby explains.

Not only did Shah Abbas foster good relations with Europe through trade, patronage and diplomacy, he also left a rich architectural and artistic legacy. This included calligraphy. Ali Riza Abbasi was the most famous calligrapher of the day and the one most favoured by the Shah.

I’ll finish with one of the many extraordinarily beautiful examples of his work here: an album of calligraphy formed like a salmon pink concertina set with pages of script. It is displayed open. The focus is on one page, a piece of poetry decorated with sprigs of golden flowers, its few lines sweeping diagonally across the page written in a cursive form of Islamic calligraphy called Nasta’liq.

I seem to have used the word beautiful rather a lot in this review. But then what can you do? It is the nature of the exhibition. On until June 14, it’s a must.