The aim of this thesis is to present various mathematical models describing human population changes in size and changes in age and sex composition due to demographic processes such as births, deaths and migrations. Models of natural growth of the population are the foundation for the development of more complicated models. By analyzing the models of sex composition in which migrations are excluded, we conclude that the only way a population could become stabilized (i.e. to have the same number of males and females) is if the birth and death rates of both sexes are equal. In natural growth models of two populations divided into age groups, we observe their age distributions when their fertility schedules or mortality schedules differ. These models do not take migrations into account and also in these models constant growth rate is assumed, so they often cannot be applied to real populations. In the last chapter, we present mathematical models which are more convenient for describing the actual changes in population. For the purpose of modeling the age composition, the population is divided into three age groups and interactions between these groups are observed. By comparing the results of linear deterministic model with the actual data of the population of Croatia, we conclude that the tested model can be employed to describe population movement in Croatia.