Conformal invariants

This master thesis investigates the moduli of families of curves and the capacities of the Gr¨otzsch and Teichm¨uller rings, which are applied in the main parts of this master thesis. The extremal properties of these rings are discussed in connection with the spherical symmetrization. Applications are given to the study of distortion of quasiconformal maps in the euclidean n-dimensional space.