THERE are several clues to the history of the early Universe. The 3-K microwave background indicates that the Universe was highly isotropic when it was about a half million years old, and the abundance of 4He (also D, 3He and 7Li) indicates that nucleosynthesis was taking place when the Universe was about three minutes old. These two facts are strong evidence that the Universe began from a hot big bang1. In addition, Hawking, Ellis and Penrose have proved (within general relativity) that the existence of the 3-K radiation implies the Universe must have been singular in its past2,3. The existence and clustering of galaxies indicate there were some deviations from homogeneity in the early Universe. Perhaps the most curious fact about the Universe is that it is composed almost entirely of matter (the Universe contains negligible amounts of antimatter) and that the number of baryons per photon (~baryon/entropy ratio) is between 10-10 and 10-8 (ref. 4). If baryon number is absolutely conserved, then it follows that the baryon number of the Universe must be viewed merely as an initial condition. Recent ideas in particle physics when applied to the early Universe may explain how an initially baryon-symmetrical (zero net baryon number) Universe could have evolved into one with net baryon number. Here, we will discuss these ideas and other interesting astrophysical implications.