Roger Penrose's original and provocative ideas about the large-scale physics of the Universe, the small-scale world of quantum physics and the physics of the mind have been the subject of controversy and discussion. These ideas were set forth in his best-selling books The Emperor's New Mind and Shadows of the Mind. In this book, he summarises and brings up to date his current thinking in these complex areas. He presents a masterful summary of those areas of physics in which he feels there are major unsolved problems. Through this, he introduces radically new concepts which he believes will be fruitful in understanding the workings of the brain and the nature of the human mind. These ideas are then challenged by three distinguished experts from different backgrounds - Abner Shimony and Nancy Cartwright as Philosophers of Science and Stephen Hawking as a Theoretical Physicist and Cosmologist. Finally, Roger Penrose responds to their thought-provoking criticisms. This volume provides an accessible, illuminating and stimulating introduction to Roger Penrose's vision of theoretical physics for the 21st Century. His enthusiasm, insight and good humour shine through this brilliant account of the problems of modern physics.