  In this paper, we classify solvable quadratic Lie algebras up to dimension 6.
In dimensions smaller than 6, we use the Witt decomposition given in
\cite{Bou59} and a result in \cite{PU07} to obtain two non-Abelian
indecomposable solvable quadratic Lie algebras. In the case of dimension 6, by
applying the method of double extension given in \cite{Kac85} and \cite{MR85}
and the classification result of singular quadratic Lie algebras in \cite{DPU},
we have three families of solvable quadratic Lie algebras which are
indecomposable and not isomorphic.
