The number of known elementary particles is now very large, and to reduce their diverse properties to order it is useful to look for symmetries between them. Symmetry properties of various kinds, and the conservation laws associated with them, are discussed here. After giving a brief survey of the general types of particle encountered in nature, we discuss first the symmetries related to space and time, and associated with the conservation laws of momentum, energy, angular momentum, and parity. Later we discuss the so-called internal symmetries, in which different particles are regarded as different states of a single basic entity. Theories of this type–particularly the ‘eightfold way’–have had considerable success in systematizing the properties of the known particles.