In the last twenty years, cosmology has unexpectedly emerged as one of the most exciting and dynamic fields of modern science. From astoundingly precise measurements of the cosmic microwave background to the ongoing mysteries of dark energy and dark matter, modern cosmology is unquestionably in the midst of its Golden Age. And yet, one of the most eminent mathematical physicists of our age, Roger Penrose is convinced that there is one fundamental problem that is consistently being overlooked: why did our universe begin in such a particular state of extremely low entropy? His Conformal Cyclic Cosmology (CCC) is an attempt to directly address that question. This extensive conversation between Howard Burton and Roger Penrose, co-recipient of the 2020 Nobel Prize in Physics and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute at the University of Oxford, explores his motivation to come up with this theory in the first place and provides detailed insights into his groundbreaking research. This carefully-edited book includes an introduction, A Hidden Audience, and questions for discussion at the end of each chapter: I. Inadvertent Success - An inside look at a mysterious publishing phenomenon II. Considering Entropy - Minimum, maximum and both at the same time III. Mysteries and False Explanations - Dark issues and inflationary hyperbole IV. Conformal Geometry - Reinterpreting the end and the beginning V. CCC: The Basic Idea - Matching beginnings and ends, conformally VI. Light Cones - Photons vs. massive particles VII. Massive Headaches - And how we might make them disappear VIII. Necessary Conditions - Dark energy, dark matter and information loss in black holes IX. Cosmic Imprints? - Searching for evidence of past aeons X. Battling Onwards - Challenges of an irrepressibly independent thinker About Ideas Roadshow Conversations Series: This book is part of an expanding series of 100+ Ideas Roadshow conversations, each one presenting a wealth of candid insights from a leading expert in a focused yet informal setting to give non-specialists a uniquely accessible window into frontline research and scholarship that wouldn't otherwise be encountered through standard lectures and textbooks. For other books in this series visit our website: https://ideas-on-film.com/ideasroadshow/.