  We classify the nilpotent almost abelian Lie algebras admitting complex or
symplectic structures. It turns out that if a nilpotent almost abelian Lie
algebra admits a complex structure, then it necessarily admits a symplectic
structure. Given an even dimensional almost abelian Lie algebra, we show that
it always admits a complex structure when it is 2-step nilpotent and it always
admits a symplectic structure when it is $k$-step nilpotent for $k=2, \, 3$ or
$4$. Several consequences of the classification theorems are obtained.
