NEXT STEPS IN OBSERVATIONAL COSMOLOGY Jeremy Mould Australian National University IfA Colloquium March 6 2000 Cosmology is the study of the large scale structure of the Universe. It was once called the quest for two numbers. The HST Key Project on the extragalactic distance scale has just reported its measurement of the first of these numbers, the Hubble Constant, to +/-10% accuracy, and this was the subject of a colloquium last year. There is also some consensus about the second number which measures the curvature of space. So is cosmology solved ? It seems more likely that we have only scratched the surface in our understanding of the expansion of the Universe. Without touching deeper questions of physical cosmology, such as inflation, there are some clear near-term projects in observational cosmology. First we look at the prospects for improving the measurement of the dimensionless quantity H_0 t_0, the product of the Hubble Constant and the age of the Universe. Second, we consider what can be learned about the evolution of large scale structure. We discuss the cosmic infrared background, the importance of redshift surveys at earlier epochs, and the implications for the instruments with which we should be equipping large ground-based telescopes.