Mats Gyllenberg addressed problems related to metapopulation dynamics. His first lecture dealt with the classical (unstructured) metapopulation model of Levins (1969). Also the relation between this model and the basic Susceptible-Infected-Susceptible model of epidemiology was mentioned. After this introduction attention shifted to structured metapopulation models, ‘structured’ here referring to differences in patch- and local population qualities. Central in this approach of metapopulations is the so-called rescue effect: an increased immigration rate between patches decreases the extinction rate of local populations. The analogy with structured population models was discussed. Several mechanisms at the local patch level (such as patch destruction, colonization, feedback mechanisms) have to be included in metapopulation models to come to a realistic point of view. As a mathematical tool to handle two basic ingredients in metapopulation models, local population growth and colonization, the semigroup formalism was presented. In the last lectures the relation of metapopulation dynamics with biodiversity and species extinction were discussed.