  We contribute to the classification of Hopf algebras with finite
Gelfand-Kirillov dimension, GK-dimension for short, through the study of
Nichols algebras over $\mathbb{D}_{\infty}$, the infinite dihedral group. We
find all the irreducible Yetter-Drinfeld modules $V$ over
$\mathbb{D}_{\infty}$, and determine which Nichols algebras $\mathcal{B}(V)$ of
$V$ are finite GK-dimensional.
