This book grew out of a short series of lectures on symmetry, aimed at a general scientific audience, given by the author at the Catholic University of Leuven, in October 1989.Using only elementary mathematics, the subtle relation between physical objects, models, and icons is discussed and some of the so-called `symmetry paradoxes' are explained. Each of the three chapters uses a case-study to show the development, through both historical and physical ideas, of someof the major concepts of symmetry.The concept and importance of an icon are strongly illustrated in the first two chapters; in Chapter 1 the origins and applications of symmetry are illustrated with the famous Orsted paradox of the interaction between the magnetic needle and the electric current. Chapter 2 deals with rotations andthe way in which Hamilton tried to describe them by means of quaternions - this gives an insight into the symmetry properties of vectors, and shows the way in which tensors and spinors gradually moved into the picture. Chapter 3 illustrates the use of symmetry in the classification of energy levelsin atoms and solids and discusses broken symmetry.