Rationality of finite groups: Groups with quadratic fields of values and related problems

The main subject of this thesis is the study of finite groups, in particular, of some connections between structural properties of groups and certain fields arising naturally from their character table. The concept of rational elements and rational groups is a classical topic in Representation Theory. In recent years, various generalization of the of rational groups were introduced, namely semi-rational groups, quadratic rational groups and inverse semi-rational groups. The latter family has aroused significant interest in the algebraic community because of equivalent formulations that connect this family of groups to different branches of mathematics. The aim of this thesis is to study the more general case of inverse semi-rational groups, called "uniformly semi-rational" and, more generally, "uniform" groups.