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The moduli problem is to describe the structure of the spaceof isomorphism classes of Riemann surfaces of a giventopological type. This space is known as the modulispace and has been at the center of pure mathematics formore than a hundred years. In spite of its age, this fieldstill attracts a lot of attention, the smooth compact Riemannsurfaces being simply complex projective algebraic curves.Therefore the moduli space of compact Riemann surfaces is alsothe moduli space of complex algebraic curves. This space lieson the intersection of many fields of

Riemann surfaces. --- Teichmüller spaces. --- Spaces, Teichmüller --- Functions of several complex variables --- Riemann surfaces --- Surfaces, Riemann --- Functions --- Teichmuller spaces.

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Complex analysis --- Functions, Theta --- Kernel functions --- Moduli theory --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Functions, Kernel --- Functions of complex variables --- Geometric function theory --- Theta functions --- Kernel functions. --- Torsion theory (Algebra) --- Torsion, Théorie de la (algèbre) --- Modules, Théorie des --- Bergman, Noyaux de --- Fonctions thêta --- Modules, Théorie des. --- Bergman, Noyaux de. --- Fonctions thêta.