After some general remarks about‘big bang’cosmology it is pointed out how, in order to explain why there is matter but no antimatter in the observed Universe, reactions involving violation of baryon number must have taken place at early times. It turns out that processes violating time reversal invariance are also necessary. The article surveys the subjects of the discrete symmetries (space inversion, time reversal and particle-antiparticle transformation) and their violation in elementary-particle physics, and grand unified theories, which predict baryon number violation. A simple model is then presented which could account qualitatively for the dominance of matter over antimatter in the Universe. It is pointed out that grand unified theories are not the only providers of a mechanism for baryon number violation; one other possibility, the sphaleron, is briefly explained.