Constants, such as the gravitational constant and the speed of light, are present in all the laws of physics. Recent observations have cast doubt on one of them. Does this mean that the structure of physics will crumble? Are we seeing the dawn of a scientific revolution? This book is written in the form of an enquiry into the importance of a possible variation in fundamental constants. Jean-Philippe Uzan and Bénédicte Leclercq ask such questions as: What is a constant? What role do constants play in the laws of physics? How can we verify that they are indeed constants? This highly instructive survey of physics, from the laboratory to the depths of space, explores the paths of gravitation, general relativity and new theories such as that of superstrings. It is complete and coherent, and goes beyond the subject of constants to explain and discuss many ideas in physics, encountering along the way, for example, such exciting details as the discovery of a natural nuclear reactor at Oklo in Gabon.