This monograph is intended for all those who are interested in membrane separation of a mixture of gases and vapors. Students of natural science or technical fields can use this as additional study material. In addition to the introduction ( Chapter 1 ) monograph contains seven additional chapters. The second chapter deals with the transport theory of gases, vapors and their mixtures by flat membranes, the third chapter deals with the separation membrane from mainly polymeric materials. Methods for determining transport parameters of gases and vapors through the membrane are described in Chap. 4th. Industrial gases and vapors division is engaged in Chap. 5 , biogas purification is in detail described in chapter 6th. The 7th chapter describe pervaporation membrane separation process of liquid mixtures, the 8th chapter discusses the membrane distillation as a progressive membrane separation process. Part of the monograph are also four appendices devoted to theoretical principles, theory, transport of gases and vapors through porous membranes and hollow fibers and interesting issues of design technology of membrane separation of gases.