Physicist Jim Al-Khalili travels through Syria, Iran, Tunisia and Spain to tell the story of the great leap in scientific knowledge that took place in the Islamic world between the 8th and 14th centuries. Its legacy is tangible, with terms like algebra, algorithm and alkali all being Arabic in origin and at the very heart of modern science - there would be no modern mathematics or physics without algebra, no computers without algorithms and no chemistry without alkalis. For Baghdad-born Al-Khalili, this is also a personal journey, and on his travels he uncovers a diverse and outward-looking culture, fascinated by learning and obsessed with science. From the great mathematician Al-Khwarizmi, who did much to establish the mathematical tradition we now know as algebra, to Ibn Sina, a pioneer of early medicine whose Canon of Medicine was still in use as recently as the 19th century, Al-Khalili pieces together a remarkable story of the often-overlooked achievements of the early medieval Islamic scientists.

To our medieval forebears the world could appear mysterious, even enchanted. Sightings of green men, dog heads and alien beings were commonplace. The world itself was a book written by God. But as the Middle Ages grew to a close, it became a place to be mastered, even exploited.

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.

Hundreds of years ago in faraway Iceland the Vikings began to write down dozens of stories called sagas - sweeping narratives based on real people and real events. But as Oxford University's Janina Ramirez discovers, these sagas are not just great works of art, they are also priceless historical documents which bring to life the Viking world. Dr Ramirez travels across glaciers and through the lava fields of Iceland to the far north west of the country to find out about one of the most compelling of these stories - the Laxdaela Saga.

Andrew Graham-Dixon begins his exploration of German art by looking at the rich and often neglected art of the German middle ages and Renaissance. He visits the towering cathedral of Cologne, a place which encapsulates the varied and often contradictory character of German art. In Munch he gets to grips with the earliest paintings of the Northern Renaissance, the woodcuts of Albrecht Durer and the cosmic visions of the painter Albrecht Altdorfer. Andrew also embarks on a tour of the Bavarian countryside, discovering some of the little-known treasures of German limewood sculpture.

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.