Macroscopic description of open dynamical systems

General scheme of the reduction of the description of open systems (with timedependent dynamical operator) is presented, which is based on the “markovised” representation of the fundamental solution and on the natural conditions of the damping of the microinformation. The simple and complete proofs of the main results of the Brussels school approach are given. The connection with the non-equilibrium statistical operator method by D.  N. Zubarev is discussed.