Definition of locally free class groups and easy consequences (e.g. if it is trivial and there is cancellation then we have NIB). Fröhlich’s conjecture at least in its consequences concerning tame abelian, dihedral, metacyclic, alternating and symmetric extensions of Q, which have normal integral basis. Introduction to associated order, first properties, towers and extensions. Sketch of partial proof of Leopoldt’s theorem. Overview on results about freeness of the ring of integers over the associated order in both local and global (local or global freeness) extensions: absolutely abelian, dihedral, metacyclic, Q8, weakly ramified extensions.