0. Summary of recent research results 2008.

1. The impact of number theoretic data on the structure of the group Gal(K_{2}K),
the group of automorphisms of the 2^{nd} Hilbert 3class field K_{2} over a quadratic field K.

1.1. Theorems concerning the impact of 3class numbers.

1.2. Theorems concerning the impact of 3capitulation.

1.3. All known examples for principalization types.

2. pring spaces not only for counting dihedral fields of degree 2p.

2.1. Halfunits in real quadratic fields.

2.2. Cubic extensions with conductor 3 or 9.

3. Current research concerning cyclic cubic fields.

3.1. Norms of primitive ambiguous principal ideals
in cyclic cubic fields with conductor divisible by two primes.
