I can also recommend Edward Frenkel's (the guest of this video) book "Love and Math" on the subject. He writes as well as he talks, the book is very approachable, not just for a mathematically literate audience, but also for those who "don't like math". Its about the Langlands Program, but also about his own personal history of becoming a mathematician in the Soviet Union and his experiences with antisemitism during that time. Fascinating Stuff, even though it only barely touches the surface of his research.