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$1$ MINIMAL k-NOIDS AND SADDLE TOWERS IN 
$\mathbb {H}^2\times \mathbb {R}$
For each 
$k\geq 3$, we construct a 
$1$-parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space 
$\mathbb {H}^2\times \mathbb {R}$ with genus 
$1$ and k embedded ends asymptotic to vertical planes. We also obtain complete minimal surfaces with genus 
$1$ and 
$2k$ ends in the quotient of 
$\mathbb {H}^2\times \mathbb {R}$ by an arbitrary vertical translation. They all have dihedral symmetry with respect to k vertical planes, as well as finite total curvature 
$-4k\pi $. Finally, we provide examples of complete properly Alexandrov-embedded minimal surfaces with finite total curvature with genus 
$1$ in quotients of 
$\mathbb {H}^2\times \mathbb {R}$ by the action of a hyperbolic or parabolic translation.
