  An almost Abelian group is a non-Abelian Lie group with a codimension 1
Abelian subgroup. This paper investigates invariant Hermitian and K\"{a}hler
structures on connected complex almost Abelian groups. We find explicit
formulas for the left and right Haar measures, the modular function, and left
and right generator vector fields on simply connected complex almost Abelian
groups. From the generator fields, we obtain invariant vector and tensor field
frames, allowing us to find an explicit form for all invariant tensor fields.
Namely, all such invariant tensor fields have constant coefficients in the
invariant frame. From this, we classify all invariant Hermitian forms on
complex simply connected almost Abelian groups, and we prove the nonexistence
of invariant K\"{a}hler forms on all such groups. Via constructions involving
the pullback of the quotient map, we extend the explicit description of
invariant Hermitian structures and the nonexistence of K\"{a}hler structures to
connected almost Abelian groups.
