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Overview and selected sample of the results and ideas formed from the formulation, analysis, and re-evaluation of mathematical models in population biology. Organized by biological theme rather than mathematical concept. Uses well-chosen and varied examples to help develop appropriate modelling skills. Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. Part II develops the theme of stage structure in an age-dependant context, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. Part III considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies.