The prevailing theory about the origin and evolution of our Universe is the so-called Big Bang theory. This is a primer in cosmological concepts. The main concepts of the Big Bang theory are.... The classic tests of the Big Bang theory make it very compelling as an apparently valid description of our universe. There are plenty of observations that highlight limitations of the Big Bang theory and point to a more detailed model of cosmology than the Big Bang theory alone provides. As discussed in the first section, the Big Bang theory predicts a range of possibilities for the structure and evolution of the universe. The final section discusses what constraints we can place on the nature of our universe based on current data, and indicates how MAP will further our understanding of cosmology. Recent observational results from the COBE satellite have revolutionized how cosmologists think about structure in the universe, and current efforts to map the fluctuations in the CMBR on smaller angular scales promise to show us details of the thermal history of the universe and to measure its fundamental parameters. Observations of large-scale structure in the universe as measured by the galaxy distribution have made dramatic progress in recent years, challenging all available theoretical models. Our knowledge of large-scale flows is still incomplete, but, when the work is finished, cosmologists will be much closer to understanding the role of dark matter in the universe. The new generation of giant telescopes such as the 10-m Keck are making remarkable observations, and the Keck, along with its newly constructed twin and the two 8-m Gemini telescopes, will enable study of the distant universe in ways never before conceivable. The HST has already made seminal contributions, including a measurement of the Hubble constant that gives the universe a surprisingly young age. We expect dramatic advances in our understanding of galaxy and large-scale structure evolution, as well as new tests of global curvature, to emerge from these studies in the coming decade. We still have no clear idea of the nature of the ubiquitous dark matter, but it is almost certainly a remnant of the early universe. Several experiments are under way to detect, or eliminate, candidates for this dark matter, and these will make substantial progress in the coming decade.