At different stages of its development, Teichmüller theory received strong impetuses from Complex analysis, geometry, and algebraic topology.It had a major impact on other fields, including low-dimensional topology, algebraic topology, hyperbolic geometry, geometric group theory, representations of discrete groups in Lie groups, symplectic geometry, theoretical physics to name a few. It also established important connections between some of the aforementioned sub-fields.
Teichmüller Theory is one of the major thrust areas in Kerala School of Mathematics.