This paper applies the methods of multi-dimensional mathematical demography to project national populations based on alternative assumptions on future, fertility, mortality, migration and educational transitions that correspond to the five shared socioeconomic pathways (SSP) storylines. In doing so it goes a significant step beyond past population scenarios in the IPCC context which considered only total population size. By differentiating the human population not only by age and sex—as is conventionally done in demographic projections—but also by different levels of educational attainment the most fundamental aspects of human development and social change are being explicitly addressed through modeling the changing composition of populations by these three important individual characteristics. The scenarios have been defined in a collaborative effort of the international Integrated Assessment Modeling community with the medium scenario following that of a major new effort by the Wittgenstein Centre for Demography and Global Human Capital (IIASA, OEAW, WU) involving over 550 experts from around the world. As a result, in terms of total world population size the trajectories resulting from the five SSPs stay very close to each other until around 2030 and by the middle of the century already a visible differentiation appears with the range between the highest (SSP3) and the lowest (SSP1) trajectories spanning 1.5 billion. The range opens up much more with the SSP3 reaching 12.6 billion in 2100 and SSP1 falling to 6.9 billion which is lower than today's world population.