  These informal notes are an expanded version of lectures on the moduli space
of elliptic curves given at Zhejiang University in July, 2008. Their goal is to
introduce and motivate basic concepts and constructions (such as orbifolds and
stacks) important in the study of moduli spaces of curves and abelian varieties
through the example of elliptic curves. The reason for working with elliptic
curves is that most constructions are elementary and explicit in this case. All
four approaches to moduli spaces of curves -- complex analytic, topological,
algebro-geometric, and number theoretic -- are considered. Topics covered
reflect my own biases. Very little, if anything, in these notes is original,
except perhaps the selection of topics and the point of view.
