I will introduce the general notion of moduli spaces and why they might be useful, focussing in particular on Teichmuller space, the moduli space of marked hyperbolic or conformal structures on a closed genus-g surface. Teichmuller theory is especially rich because it draws on tools from both hyperbolic geometry and complex analysis, and serves as a prototype for many other moduli spaces; we will highlight some examples of this in the talk. Speaker(s): Feng Zhu (UM)