Different information sources, namely National Strategy for Higher Education to 2030 (Ireland), Introduction to Primary School Curriculum (1999), (Ireland), Primary Professional Development Service--Differentiation in Action, Ireland's official postgraduate study website, the Strategic Plan 2012-2016 of Mary Immaculate College, Limerick University), have been studied. The mission of primary education in the light of differentiating teaching has been indicated. Main aspects of differentiating teaching have been highlighted. The correspondence between differentiating teaching foundations and primary school curriculum has been proved. Irish experience in professional training of future primary teachers in the system of postgraduate education in the light of differentiating teaching has been analyzed. Due to theoretical analysis of Professional Master of Education (Primary Teaching) (PME) postgraduate course's aims the priority tasks of future primary teachers have been defined. Peculiarities of the postgraduate course of the Professional Master of Education (Primary Teaching) at Mary Immaculate College, University of Limerick have been justified. Positive aspects of Irish experience in postgraduate education system, in particular professional training of primary teachers, have been defined. Perspectives for the Ukrainian postgraduate system as for professional training of primary teachers have been outlined.