The spectral geometry of Riemann surfaces

This chapter is spread out over a number of papers and also builds on my earlier work on the relationship between the spectral geometry of manifolds and the spectral geometry of graphs. It seemed to be a reasonable idea to put together these ideas in one overall framework, which will be accessible to someone at the graduate level. The material naturally breaks up into a number of areas, each one having connections to basic graduate material, but putting these different pieces together demands a fair amount of breadth. We hope to supply this breadth in the chapters.