This is a course of lectures given for students of the Regional Mathematical Center of the Novosibirsk State University from October 20 to November 3, 2017. The course is devoted to some geometric problems of ramified coverings of the Riemann sphere. A special attention is payed to compact surfaces of genus one (complex tori). In the first section we give a short introduction to the theory of elliptic functions. Section 2 is devoted to one-parametric families of holomorphic and meromorphic functions. We recall the role of such families on Loewner's equation in solving some problems of the theory of univalent functions. Further we deduce a system of ODEs expressing dependence of critical points of a family of rational functions from their critical values. This gives an approximate method to find a conformal mapping of the Riemann sphere onto a given simply-connected compact Riemann surface over the sphere. Thereafter a similar problem is solved for elliptic functions uniformizing comple 查看全文>>