Nowadays we can apply simple potential models, formerly used by nuclear physicists to describe magic numbers of atomic nuclei, in a more sophisticated version to calculate with the same success electronic shell structures of metal clusters especially of alkali metals. By means of such a model, optimized for alkali metal clusters, the experimentally observed magic numbers can be explained up to 1432 electrons. We have used the ''aufbau principle'' generated from this model to construct a Periodic System of Alkali Metal Clusters (PSC) which differ significantly from the well-known Periodic System of Elements (PSE). It exhibits not only 18 main groups and very many subgroups with high values of angular momentum quantum number, but it is an open periodic system because of no sort of restriction as to the cluster size. In analogy to the PSE, we succeeded in deriving informations on the ''chemistry of alkali metal clusters'' from the PSC, using two different concepts of clusters: (1) clusters = molecules and (2) clusters = giant atoms. Especially the second point of view gives interesting and possible, but speculative results as to various forms of ''cluster-matter'' like ''cluster-molecules'', ''cluster-crystals'', ''cluster-metals'' etc. up to new materials. We hope, these speculations will give many thought-provoking impulses both for new experiments and for new calculations.