Constants, such as the gravitational constant and the speed of light, are present in all the laws of physics, yet recent observations have cast doubt on one of them. This book examines constants, the role they play in the laws of physics, and whether indeed constants can be verified. The authors provide an overview of the history of the ideas of physics, evoking major discoveries from Galileo and Newton to Planck and Einstein and raising questions provoked by ever more current accurate observations. They investigate the solidity of the foundations of physics and discuss the implications of the discovery of the non-constancy of a constant. From the laboratory to the depths of space, this highly instructive survey explores the paths of gravitation, general relativity and new theories such as that of superstrings. It even 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--