The Great Pyramid of Giza's construction is still shrouded in mystery, despite it being the only survivor among the Seven Wonders of the Ancient World. In Building the Great Pyramid, travel back 4,500 years with the BBC as they re-create the circumstances under which it may have been built, as well as the daily life of the population at that time. Expert archaeologists, Egyptologists, and scholars share their latest theories on what may have happened. The film combines dramatic reconstruction, location shooting and state-of-the-art CGI computer effects. Directed and written by Jonathan Stamp.

Horizon discovers what your cat really gets up to when it leaves the cat flap. In a groundbreaking experiment, 50 cats from a village in Surrey are tagged with GPS collars and their every movement is recorded, day and night, as they hunt in our backyards and patrol the garden fences and hedgerows. Cats are fitted with specially developed cat-cams which reveal their unique view of our world. You may think you understand your pet, but their secret life is more surprising than we thought.

We live our lives pursuing happiness 'out there' as if it is a commodity. We have become slaves to our own desires and craving. Happiness isn't something that can be pursued or purchased like a cheap suit. This is Maya, illusion, the endless play of form. In the Buddhist tradition, Samsara, or the endless cycle of suffering is perpetuated by the craving of pleasure and aversion to pain. Freud referred to this as the "pleasure principle." Everything we do is an attempt to create pleasure, to gain something that we want, or to push away something that is undesirable that we don't want. Even a simple organism like the paramecium does this. It is called response to stimulus. Unlike a paramecium, humans have more choice. We are free to think, and that is the heart of the problem. It is the thinking about what we want that has gotten out of control. The dilemma of modern society is that we seek to understand the world, not in terms of archaic inner consciousness, but by quantifying and qualifying what we perceive to be the external world by using scientific means and thought. Thinking has only led to more thinking and more questions. We seek to know the innermost forces which create the world and guide its course. But we conceive of this essence as outside of ourselves, not as a living thing, intrinsic to our own nature. It was the famous psychiatrist Carl Jung who said, "one who looks outside dreams, one who looks inside awakes." It is not wrong to desire to be awake, to be happy. What is wrong is to look for happiness outside when it can only be found inside.

In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

Two thousand years ago one of history's most notorious individuals was born. Professor Mary Beard embarks on an investigative journey to explore the life and times of Gaius Julius Caesar Augustus Germanicus - better known to us as Caligula. Caligula has now become known as Rome's most capricious tyrant, and the stories told about him are some of the most extraordinary told about any Roman emperor. He was said to have made his horse a consul, proclaimed himself a living God, and indulged in scandalous orgies - even with his own three sisters - and that's before you mention building vast bridges across land and sea, prostituting senators' wives and killing half the Roman elite seemingly on a whim. All that in just four short years in power before a violent and speedy assassination in a back alley of his own palace at just 28-years-old." But how much of his story is true? Travelling across the Roman world - from Germany and Capri in the bay of Naples to the astonishing luxury of his life in imperial Rome - Mary attempts to peel away the myths. Some stories are difficult to get to the bottom of as they were written by hacks long after his death, but there is plenty of surviving evidence where the 'real' Caligula can be glimpsed. Such as in the extraordinary luxury of his private yachts outside Rome; in the designs he chose for his coins when he became Emperor; in an eye-witness account of Caligula's withering humour written in 41AD; the trial documents covering the mysterious death of his father when he was just seven-years-old; and even in a record of his imperial slaves - from the palace spy to his personal trainer. Piecing together the evidence, Mary puts Caligula back into the context of his times to reveal an astonishing story of murder, intrigue and dynastic family power. Above all, she explains why Caligula has ended up with such a seemingly unredeemable reputation. In the process, she reveals a more intriguing portrait of not just the monster, but the man.

Sagan discusses the story of the Heike crab and artificial selection of crabs resembling samurai warriors, as an opening into a larger discussion of evolution through natural selection (and the pitfalls of intelligent design). Among the topics are the development of life on the Cosmic Calendar and the Cambrian explosion; the function of DNA in growth; genetic replication, repairs, and mutation; the common biochemistry of terrestrial organisms; the creation of the molecules of life in the Miller-Urey experiment; and speculation on alien life (such as life in Jupiter's clouds). In the Cosmos Update ten years later, Sagan remarks on RNA also controlling chemical reactions and reproducing itself and the different roles of comets (potentially carrying organic molecules or causing the Cretaceous–Paleogene extinction event).