We classify the almost abelian Lie algebras \({\mathfrak {g}}_A={{\mathbb {R}}}e_0 \ltimes _A {{\mathbb {R}}}^{2n-1}\) admitting complex or symplectic structures. The matrix \(A\in M(2n-1,{{\mathbb {R}}})\) encodes the adjoint action of \(e_0\) on the abelian ideal \({{\mathbb {R}}}^{2n-1}\) , and the existence of complex or symplectic structures on \({\mathfrak {g}}_A\) imposes restrictions on the Jordan normal form of A. The classification essentially reduces to the case when A is nilpotent, so we start by considering this case. It turns out that if A is nilpotent and \({\mathfrak {g}}_A\) admits a complex structure, then \({\mathfrak {g}}_A\) necessarily admits a symplectic structure. This is not true in general when A is non-nilpotent. Finally, several consequences of the classification theorems are obtained.
