  We consider a general concept of composition and decomposition of objects,
and discuss a few natural properties one may expect from a reasonable choice
thereof. It will be demonstrated how this leads to multiplication and co-
multiplication laws, thereby providing a generic scheme furnishing
combinatorial classes with an algebraic structure. The paper is meant as a
gentle introduction to the concepts of composition and decomposition with the
emphasis on combinatorial origin of the ensuing algebraic constructions.
