Population dynamics studies changes in the size and composition of populations over time. Ordinary differential equations are well suited for modelling both the change of one species and of several species. The present work gives an overview of the most popular mathematical population models. It starts with the simplest one-dimensional models and initially goes into two-dimensional systems. The basic types of biological interactions are analyzed: predator-prey, competition and mutualism. Each model is complemented by a mathematical analysis, which explains the behavior respectively the long-term behavior of the solutions as well as visualizing them in graphics and giving biological interpretations. Finally, the paper discusses models with n different populations and gives an outlook on more general models.