In this paper we review the current status of cosmological theory. First a brief discussion of Friedmann model and classical observations is presented. Next the events of the early Universe from a fraction of a second to the present are discussed from the point of view of high temperature thermodynamics. The most important phenomena in this phase are pair creation of particles and nuclear equilibrium at temperatures 10^9 K and above. When the temperature drops, nuclear equilibrium will freeze out, resulting in the synthesis of helium and some light elements. Likewise pairs of particles will annihilate at lower temperatures but some relic particles may remain intact today. So far the theory seems to be on solid ground. However, there are many unanswered questions which force one to make certain drastic assumptions, such as the existence of dark (invisible) matter. One is also forced to retrace the evolution of the Universe back in time to 10^-36 second, during which quantum effects of gravity become important. This then leads to the Inflationary Theory. This theory is still under development. Scanty data exist to support or to refute the theory. The origin of our Universe - the ultimate frontier in astrophysics and a Pandora Box - is now open for exploration.