Prof. Bruno Zumino, Physics Dept., UC Berkeley discusses symmetries, which play a very important role in nature. Some of these (e.g. mirror symmetry, time reversal and the symmetry that relates particles to antiparticles) are described by discrete transformations. These are not independent of one another, but are related by an important property of space-time that is implied by Einstein's theory of relativity. Other symmetries involve smooth transformations; some are only approximately valid, but are still very useful for an understanding of nature. There are also speculated symmetries, of which the most important is called supersymmetry, and relates the properties of very different particles. In spite of the lack of direct experimental evidence, there are compelling arguments for its validity. In theories such as string theory that attempt to unify quantum mechanics with Einstein's gravity, a new concept emerges to replace in part that of symmetry, the concept of duality.