This programme describes the Red Army's dramatic advance and the German's brutal resistance. Witnesses reveal how the final days of the conflict were barbarous almost beyond comprehension.

Part 2 examines how the freewheeling modernism that had shocked audiences in the first two decades of the century came under state control. Initially, many practitioners thought the totalitarian regimes would be good for music and the arts. What followed in Germany was a ban on music written by Jews, African-Americans and communists, while in the Soviet Union there was a prohibition on music the workers were unable to hum. After the cataclysm of the 1940s, a new generation of composers - Boulez, Stockhausen, Xenakis, Nono, Ligeti - turned their back on what they saw as the discredited music of the past and tried to reinvent it from scratch. Or, at least, from serialism, which became as much of a straitjacket as totalitarianism's strictures had been. But from this period of avant-garde experimentation, which many listeners found baffling and terrifying, came some of the most influential and radical musical innovations of the century.

Marcus Du Sautoy wants to find out how close we are to creating machines that can think like us: robots or computers that have artificial intelligence. His journey takes him to a strange and bizarre world where AI is now taking shape. Marcus meets two robots who are developing their own private language, and attempts to communicate to them. He discovers how a super computer beat humans at one of the toughest quiz shows on the planet, Jeopardy". And finds out if machines can have creativity and intuition like us. Marcus is worried that if machines can think like us, then he will be out of business. But his conclusion is that AI machines may surprise us with their own distinct way of thinking.

Dr Aleks Krotoski concludes her investigation of how the World Wide Web is transforming almost every aspect of our lives. Joined by Facebook founder Mark Zuckerberg, Bill Gates, Al Gore and the neuroscientist Susan Greenfield, Aleks examines the popularity of social networks such as Facebook and asks how they are changing our relationships. And, in a ground-breaking test at University College London, Aleks investigates how the Web may be distracting and overloading our brains.

Fish dominate the planet's waters through their astonishing variety of shape and behaviour. The beautiful weedy sea dragon looks like a creature from a fairytale, and the male protects their eggs by carrying them on his tail for months. The sarcastic fringehead, meanwhile, appears to turn its head inside out when it fights. Slow-motion cameras show the flying fish gliding through the air like a flock of birds and capture the world's fastest swimmer, the sailfish, plucking sardines from a shoal at 70 mph. And the tiny Hawaiian goby undertakes one of nature's most daunting journeys, climbing a massive waterfall to find safe pools for breeding.

Marcus du Sautoy uncovers the patterns that explain the shape of the world around us. Starting at the hexagonal columns of Northern Ireland's Giant's Causeway, he discovers the code underpinning the extraordinary order found in nature - from rock formations to honeycomb and from salt crystals to soap bubbles. Marcus also reveals the mysterious code that governs the apparent randomness of mountains, clouds and trees and explores how this not only could be the key to Jackson Pollock's success, but has also helped breathe life into hugely successful movie animations.