  Among the large variety of two-dimensional (2D) materials discovered to date,
elemental monolayers that host superconductivity are very rare. Using ab initio
calculations we show that recently synthesized gallium monolayers, coined
gallenene, are intrinsically superconducting through electron-phonon coupling.
We reveal that Ga-100 gallenene, a planar monolayer isostructural with
graphene, is the structurally simplest 2D superconductor to date, furthermore
hosting topological edge states due to its honeycomb structure. Our anisotropic
Eliashberg calculations show distinctly three-gap superconductivity in Ga-100,
in contrast to the alternative buckled Ga-010 gallenene which presents a single
anisotropic superconducting gap. Strikingly, the critical temperature ($T_c$)
of gallenene is in the range of $7-10$ K, exceeding the $T_c$ of bulk gallium
from which it is exfoliated. Finally we explore chemical functionalization of
gallenene with hydrogen, and report induced multigap superconductivity with an
enhanced $T_c$ in the resulting gallenane compound.
