The course will serve as an introduction to mathematical modelling of biological processes. It will cover a selection of the following topics: Difference equations and applications. Linear differential equations and systems; phase plane analysis; nonlinear systems of differential equations and linearization; Poincaré-Bendixson Theorem. Applications of differential equations to biology, including a logistic population with harvesting; predator-prey model; competing species; epidemic models. Examples of partial differential equations; reaction-diffusion equation; pattern formation.