Julian Richards recalls how, after years of raiding, England's resistance was so weakened that, in the early 11th century, the Vikings were finally able to seize the throne. In other parts of the British Isles however, they gained and maintained power by integration.

Andrew Graham-Dixon travels to Istanbul to immerse himself in the tumultuous world of the Byzantine Empire. He decodes the iconography of the art of the period and explains its continuing relevance.

The tale of one of China's most famous dynasties begins with the amazing story of Hongwu, a peasant rebel who founded one of greatest eras in Chinese history. The film takes us to his great capital Nanjing, with its 21 miles of walls, each brick stamped with the name of the village that made it. Following the trail, we go to the Bao family village and see the villagers act a Ming murder story.
Like many authoritarian states, the Ming were obsessive about architecture. We see the giant fortifications of the Great Wall, the ritual enclaves of the Forbidden City in Beijing and travel with bargeman Mr Hu down the Grand Canal, China's great artery of commerce right up to the present day. We then hear about Admiral Zheng He's voyages to Africa and the Gulf decades before Columbus, watch the construction of an ocean-going wooden boat 250ft long, and hitch a ride on a replica Ming junk in the South China Sea.
As state prosperity grew, so did a rising middle class. Wood looks at Ming culture in Suzhou, the 'Venice of China'. Staying in a merchant's house, he discovers the silk, ceramic and lacquer-making industries, and visits one of the most beautiful gardens in the city. Then on to Macao and the arrival of Jesuit missionary Matteo Ricci, who hoped to convert China to Christianity. In the cathedral in Beijing, we learn more about these fateful exchanges with the west. Finally in Shaoxing, we visit the house of the 'Ming Proust' and at grassroots the Zhao family in Fujian where the film ends in an elegiac mood with the fall of the Ming in 1644.

The story of the Viking world's most famous warrior, the legend of Beowulf is the ultimate tale of courage. Pit against thirsty invaders, barbaric monsters and a fire breathing dragon, Beowulf emerges as Norse mythology's greatest hero. But could this warrior have actually been real? Unearthed burial mounds and ancient carvings suggest the myth of Beowulf might have been more than epic legend.

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. In the second episode, Du Sautoy explores how maths helped build imperial China and discovers how the symbol for the number zero was invented in India. He also looks at the Middle Eastern invention of algebra and how mathematicians such as Fibonacci spread Eastern knowledge to the West.

Julian Richards investigates the impact of the Vikings in Britain. This edition focuses on the archaeological trail left by the Vikings as they travelled from Norway along the sea road to Dublin. Settlements, a boat burial and evidence of trading have been discovered on the Scottish isles, and silver hoards found in Ireland suggest that Dublin was not only wealthy and important, but also a centre for trade in slaves.