What is "Teichmüller Theory" ? What part has been worked out / forseen by O. Teichmüller himself and what is further development ? Is there some current work which might be considered as continuation/completion of this theory ?
Background The question might be seen as too naive and can be answered by google or Wikipedia, but I have it in mind for a long time and do not think that it is that much simple. Let me explain what is puzzling me: Teichmüller space is very close to moduli space of Riemann surfaces ("The Teichmüller space is the universal covering orbifold of the (Riemann) moduli space.") and reading some sources make me expression that "Teichmüller Theory" is everything which is related to the moduli space of Riemann surfaces. Is it really like this ? If it is true it does not seem to me good name since "theory" should be something not so diverse as current research on moduli spaces of Riemann surfaces.
On the other hand what I heard about the contribution of Teichmüller himself - it is introduction of the Teichmüller metric by means of quasiconformal maps. (See Wikipedia). It is beautiful result, but it is kind of "theorem", not "theory", so probably there is something more ? which I am missing ?
The question might be considered as background to What are some Applications of Teichmüller Theory?