This paper gives some introductory notes on multi-criterion decision making. It addresses to the known division into models of multi-purpose decision making and multi-attribution decision making or multi-criterion analysis, general notion of models, terminology, taxonomy of methods as well as significance of interactive methods and the role of a decision maker in the procedure of solution making. The first out of a set of significant facets of implementation of multi-criterion decision making models is shown further: marginal solutions and their consequences, that is an examination of a possibility of perfect solution of the said model.