Problems in hypermap theory have applications to many branches of mathematics. This is a consequence of the different interpretations of the notion of a hypermap. A hypermap is

-A representation of a hypergraph (Combinatorics);
-A triangulation of a compact surface (Topology);
-A quotient of an isometry group of the hyperbolic plane (Algebra/Geometry);
-A Riemann surface (Analysis/Geometry).

In this talk I will present some technics used by solving problems of the following kind:
-Given a hypergraph, classify all the corresponding hypermaps (with a certain property).
-Given a topological surface, classify all the corresponding hypermaps (with a certain property).
-Identify hypermaps corresponding to the same Riemann surface.