Procyclic Galois Extensions of Algebraic Number Fields

The main theme of this thesis is the existence and properties of Galois extensions of algebraic number fields with Galois group isomorphic to the additive group of p-adic integers, in short procyclic extensions. However, extensions with non-abelian pro-p-groups as Galois groups are also considered. The connection between procyclic extensions and Leopoldt''s Conjecture is discussed. The notion of p-rationality is defined, and the classification of 2-rational imaginary quadratic fields is given, apparently for the first time (correctly).