It's intrumental for teaching. We see every day how difficult it is for the newcomer to grasp the idea of a Riemann surface and how he owns the whole theory once he has understood this fundamental concept. F. Klein Jahresber. It's a popular subject.
Computer algebra meets analytic functions.
Poster Photograph Interactive 3D graphics and contour integral representations of special functions. Choose the imaginary part of as a representation of the Riemann surface. Use natural parametrization.