  We investigate Lie algebras endowed with a complex symplectic structure and
develop a method, called \emph{complex symplectic oxidation}, to construct
certain complex symplectic Lie algebras of dimension $4n+4$ from those of
dimension $4n$. We specialize this construction to the nilpotent case and apply
complex symplectic oxidation to classify eight-dimensional nilpotent complex
symplectic Lie algebras.
