Lattices in solvable Lie groups and deformations of homogeneous spaces

The space $\mathrm{SD}_n$ of pairs $(S,\Gamma)$ is studied, where $S$ is a solvable simply-connected Lie group and $\Gamma$ is a lattice in $S$, considered up to isomorphism. The structure of a neighborhood of a point $(S,\Gamma)\in\mathrm{SD}_n$ is described for two classes of groups $S$. In this connection deformations of homogeneous spaces are studied. Homogeneous spaces of type $K(\pi,1)$ are studied in the Appendix.
Bibliography: 14 titles.