Is the universe infinite, or does it have an edge beyond which there is, quite literally, nothing? Do we live in the only possible universe? Why does it have one time and three space dimensions - or does it? What is it made of? What does it mean when we hear that a new particle has been discovered? Will quantum mechanics eventually break down and give way to a totally new description of the world, one whose features we cannot even begin to imagine? This book aims to give the non-specialist reader a general overview of what physicists think they do and do not know in some representative frontier areas of contemporary physics. After sketching out the historical background, A. J. Leggett goes on to discuss the current situation and some of the open problems of cosmology, high-energy physics, and condensed-matter physics. Unlike most other accounts, this book focuses not so much on recent achievements as on the fundamental problems at the heart of the subject, and emphasizes the provisional nature of our present understanding of things.