The rich and unique properties of the stage-n graphite alkali-metal-intercalation compounds are fully investigated by first-principles calculations. According to the main features, the lithium and non-lithium (Na, K, Rb, Cs) systems are quite different from each other in stacking configurations, intercalant alkali-metal-atom concentrations, free conduction electron densities, atom-dominated and (carbon, alkali metal)-co-dominated energy bands, and interlayer charge density distributions. The close relations between the alkali-metal-doped metallic behaviors and the geometric symmetries are clarified through the interlayer atomic interactions. The stage-1 graphite alkali-metal-intercalation compounds possess the highest charge distribution for all stage-n types; moreover, those of the lithium systems are greater than those of the non-lithium systems. The lithium systems also have the largest blue shift of the Fermi level among all alkali metal systems.