An introduction to mathematical modelling of complex biological systems. The primary focus will be on sets of chemical reactions arising in biological contexts (for example, in gene regulation). Such sets of coupled reactions give rise to mathematical models that display nonlinear and stochastic behaviour. The course will provide a survey and practical introduction to the mathematical techniques used in modelling, simulating, and analyzing such systems, including nonlinear dynamics as well as Monte Carlo and other simulation techniques for stochastic systems. Although examples will be drawn mainly from biochemical systems, the techniques discussed will be applicable to many systems in physics, chemistry, and biology. The course will be presented in a self-contained and pragmatic manner aimed at providing an applied introduction to these mathematical techniques to a potentially interdisciplinary audience.