  This paper concerns the problem of classifying finite-dimensional real
solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the
one hand, we present an effective method to classify all $(n+1)$-dimensional
real solvable Lie algebras having 1-codimensional derived algebras provided
that a full classification of $n$-dimensional nilpotent Lie algebras is given.
On the other hand, the problem of classifying all $(n+2)$-dimensional real
solvable Lie algebras having 2-codimensional derived algebras is proved to be
wild. In this case, we provide a method to classify a subclass of the
considered Lie algebras which are extended from their derived algebras by a
pair of derivations containing at least one inner derivation.
