1. Introduction 2. Determination of the isometry group of a Riemannian group manifold 3. Solvable Lie algebras of negative curvature type 4. De Rham decomposition of solvmanifolds 5. Simply transitive subgroups and Levi decompositions of the isometry group 6. Relations between simply transitive subgroups of the isometry group 7. Stabilizers and complete isometry algebras 8. Constructions of metrics with negative curvature 9. Characterization of full isometry groups