  A nilmanifold resp. solvmanifold is a compact homogeneous space of a
connected and simply-connected nilpotent resp. solvable Lie group by a lattice,
i.e. a discrete co-compact subgroup.
  There is an easy criterion for nilpotent Lie groups which enables one to
decide whether there is a lattice or not. Moreover, it is easy to decide
whether a nilmanifold is formal, Kaehlerian or (Hard) Lefschetz.
  The study of solvmanifolds meets with noticeably greater obstacles than the
study of nilmanifolds. Even the construction of solvmanifolds is considerably
more difficult than is the case for nilmanifolds. The reason is that there is
no simple criterion for the existence of a lattice in a connected and
simply-connected solvable Lie group.
  We consider the question of existence of lattices in solvable Lie groups up
to dimension six and examine whether the corresponding solvmanifolds are
formal, symplectic, Kaehler or (Hard) Lefschetz.
