The main contributions of this doctoral thesis are: 1. Alexander's method for infinite-type surfaces. For any infinite-type surface S possibly with non-empty boundary, there exist a collection τ of essential curves and ...

In this work we prove: 1) every orientable topological surface without boundary and finite genus admits at least one (in fact, uncountably many) Riemann surface structure, such that the group of quasiconformal homeomorphisms ...