The course introduces basic mathematical tools and software used in modeling and analysis of complex systems. Mathematical models are used to describe and understand the dynamics of real-world systems in essentially all applied sciences, such as physics, biology, chemistry, engineering, economics, social sciences etc. The theory of system dynamics is compact, intuitive and very powerful, and relies fundamentally on numerical integration of coupled ordinary differential equations (ODE). The course will cover concepts like integration methods, feedback, modeling artefacts, mechanistic and descriptive modeling, stochasticity, parameter optimization, Monte Carlo simulations and chaotic systems. In this hands-on course we will model and implement dynamical systems, understand the theoretical background and limitations, and practice understanding and communicating of models. The course assessment is a documented model of a case study conceived by the student.