Shimizu and Ueno (no credentials listed) consider several aspects of the moduli theory from a complex analytic point of view. They provide a brief introduction to the Kodaira-Spencer deformation theory, Torelli's theorem, Hodge theory, and non-abelian conformal theory as formulated by Tsuchiya, Ueno, and Yamada. They also discuss the relation of non-abelian conformal field theory to the moduli of vector bundles on a closed Riemann surface, and show how to construct the moduli theory of polarized abelian varieties.