Projection formalism in the kinetic theory

The compact projection technique for the derivation of the kinetic equations from the BBGKY-hierarchy is presented, which is suitable, in particular, for the description of the inhomogeneous systems. The projector (defined constructively) provides the possibility to treat the formally linear problem at all the intermediate steps. The method permits one to derive the kinetic equations in a unified manner in different physical situations defined by the choice of one or another small parameter. As an illustration, the density expansion is considered.