  We continue the algebraic study of almost inner derivations of Lie algebras
over a field of characteristic zero and determine these derivations for free
nilpotent Lie algebras, for almost abelian Lie algebras, for Lie algebras whose
solvable radical is abelian and for several classes of filiform nilpotent Lie
algebras. We find a family of $n$-dimensional characteristically nilpotent
filiform Lie algebras $\mathfrak{f}_n$, for all $n\ge 13$, all of whose
derivations are almost inner. Finally we compare the almost inner derivations
of Lie algebras considered over two different fields $K\supseteq k$ for a
finite-dimensional field extension.
