The title of Ava DuVernay's extraordinary and galvanizing documentary refers to the 13th Amendment to the Constitution, which reads 'Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States.' The progression from that second qualifying clause to the horrors of mass criminalization and the sprawling American prison industry is laid out by DuVernay with bracing lucidity. With a potent mixture of archival footage and testimony from a dazzling array of activists, politicians, historians, and formerly incarcerated women and men, DuVernay creates a work of grand historical synthesis.

It's this moment where now both sides realize that no quarter will be asked, and no quarter will be given. Surrender is no longer even an option. You're in this to the end. You either die or you triumph, and there is no other alternative. Amid a spiral of brutality and low morale, Mehmed makes Giustiniani an enticing offer. The grand vizier urges Mehmed to seek a truce with his rival.

Is mankind alone, or are there aliens out there, either waiting to be discovered, or on their way to find Earth? Professor Brian Cox spends this episode asking such questions, and what he discovers may raise a few eyebrows. He begins by exploring the human race's efforts to find neighbours in outer space, including the launch of two golden discs containing a greeting from Earth in the 1970s; they are still travelling and are now the most distant man-made objects from the planet. Brian also meets members of the Search for Extra-Terrestrial Intelligence, who have been monitoring radio signals for 50 years without success, before discussing the ingredients needed to make an intelligent civilisation with astrophysicist Dr Frank Drake.

After more than a century of civil war, Toyotomi Hideyoshi has united Japan. His rivals have either sworn their allegiance, or they have been destroyed. Despite this fledgling peace, Hideyoshi now dreams of a bold and outlandish plan to make himself the most powerful man in Asia. He plans to expand his reign to China. Logistical challenges and fierce operation in Korea prove to be costly.

The Cave of Swallows in Mexico is a 400m vertical shaft, deep enough to engulf the Empire State Building. The Lechuguilla cave system in the USA is 193km long and 500m deep with astonishing crystal formations hanging from its chambers. Although often overlooked, caves are remarkable habitats with equally bizarre wildlife. Cave angel fish cling to the walls behind cave waterfalls with microscopic hooks on their flattened fins. Cave swiftlets navigate by echo-location and build nests out of saliva. The Texas cave salamander has neither eyes nor pigment. Unique access to a hidden world of stalactites, stalagmites, snotites and troglodytes brings a wealth of surprises.

Every year, over a thousand climbers try to reach the summit of Mount Everest, with the annual record for successful attempts currently standing at 633. But of that number, nearly half were Sherpas - the mountain's unsung heroes. Yet the Sherpa community has remained secretive about their nation, culture and experiences living in the shadow of the world's highest mountain. Now, for the first time, they open the door into their world. Without the expertise of the Sherpas, only the hardiest and most skilful climbers would succeed. Every day they risk their lives for the safety of others, yet they seek neither glory nor reward, preferring to stay in the background. Following the stories of four such Sherpas - Phurba, Ngima, Ngima Tenji and Gelu - this film reveals the reality of their daily lives, not just up the mountain, but with their families after they return home.