  Results about the following classes of finite-dimensional Lie algebras over a
field of characteristic zero are presented: anisotropic (i.e., Lie algebras for
which each adjoint operator is semisimple), regular (i.e., Lie algebras in
which each nonzero element is regular in the sense of Bourbaki), minimal
nonabelian (i.e., nonabelian Lie algebras all whose proper subalgebras are
abelian), and algebras of depth 2 (i.e., Lie algebras all whose proper
subalgebras are abelian or minimal nonabelian).
