Our current understanding of the evolution of the Universe is based upon the Friedmann-Robertson-Walker (FRW) cosmological model, or the hot big bang model as it is usually called. The model is so successful that it has become known as the standard cosmology. In this first Chapter we will review the observational basis for the standard cosmology. Direct evidence supporting its validity extends back to the beginning of the epoch of primordial nucleosynthesis, about 10–2 sec after the bang. Current speculations about the earliest history of the Universe, the subject of this monograph, derive from an extrapolation of the standard cosmology to very early times. The FRW cosmology is so robust that it is possible to make sensible speculations about the Universe at times as early as 10–43 sec after the bang! Of course, such speculations are necessarily based upon some theory of the fundamental interactions at very high energies, energies approaching the Planck scale (1019 GeV). At present there exists a standard model of particle physics, the SU(3)c⊗ SU(2) L ⊗ U(1) Y gauge theory of the strong and electroweak interactions. It provides a fundamental theory of quarks and leptons and has been tested up to energies approaching 1000 GeV. In addition, the past decade has produced very interesting and important speculations about particle physics at very short distances, e.g., grand unification, supersymmetry, superstring theory, etc. It is these theories of fundamental physics at ultra-high energies which allow us to speculate about the earliest history of the Universe.