  Alkali metal atoms (Li, Na, K, Rb, Cs), dimers and (2$\times$2) monolayers on
a graphite (0001) surface have been studied using density functional theory,
pseudopotentials, and a periodic substrate. The adatoms bind at the hollow site
(graphite hexagon), with Li lying closest to (1.84 \AA) and Cs farthest (3.75
{\AA}) from the surface. The adsorption energies range between $0.55-1.21$ eV,
and the energy ordering of the alkali adatoms is Li$>$Cs$\ge$Rb$\ge$K$>$Na. The
small diffusion barriers (0.02-0.21 eV for the C-C bridge) decrease as the atom
size increases, indicating a flat potential energy surface. The formation
(cohesion) energies of (2$\times$2) monolayers range between 0.55-0.81 eV,
where K has the largest value, and increased coverage weakens the
adsorbate-substrate interaction (decoupling) while a two-dimensional metallic
film is formed. Analysis of the charge density redistribution upon adsorption
shows that the alkali metal adatoms donate a charge of $0.4-0.5 e$ to graphite,
and the corresponding values for (2$\times$2) monolayers are $\sim 0.1 e$ per
atom. The transferred charge resides mostly in the $\pi$-bands (atomic
$p_z$-orbitals) of the outermost graphene layer.
