Abstract
The paper begins with a brief account of Christoffel’s work on abelian integrals and its historical context and then describes the close connection between Riemann surfaces and Fuchsian groups. This is followed by a survey of some modern developments in the theory of infinitely generated Fuchsian groups, namely the Bers spaces (the generalization of the space of abelian differentials) and the classification of Fuchsian groups.
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