The authors present a review of findings pertaining to the transplantation of haematopoietic stem cells of the peripheral blood. They pay particular attention to the theoretical basis of this transplantation, its history and technical procedure. The selection of literature concentrates on important original work. The whole problem was divided into three parts. In the first part the authors pay attention to haematopoiesis, cultivation of haematopoietic cells and the discovery of haematopoietic stem cells of the peripheral blood.