The mathematical modeling of real-life phenomena in the natural, engineering, and social sciences often involve having to solve systems of difference or differential equations. These systems are inherently complex, owing to their (typically) high dimensionality and nonlinearity. Hence, their exact solutions are difficult (if at all feasible) to obtain. Consequently, these systems are generally studied using a combination of asymptotic analysis and numerical discretization approaches. This course will cover a broad spectrum of techniques, theories and tools for modeling and analysing real-life phenomena arising in population biology, with emphasis on the study and asymptotic analysis of general classes of unstructured (single species discrete-time and continuous-time models, interacting populations etc.) and structured (spatially-structured, age-structured, sex-structured) population biology models arising in ecology and epidemiology.