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The study of Dynamical Systems explores how systems evolve over time, focusing on the long-term behavior of these systems under different conditions. It provides the mathematical framework to analyze how a system's state changes as a function of time, which can model a wide range of real-world phenomena, from physical and biological processes to economics and engineering applications. Dynamical Systems is delivered mainly through lectures backed up by tutorial sessions. The lecture includes interactive elements whereby students in groups apply principles to simple problems to ensure their involvement and so gain understanding. Handouts are used so that students can concentrate on the material of the lecture, but with gaps where students either have to fill in or make separate notes. Problem sheets will be given out to students and after time, the problems will be discussed in class. The assignment will require the students to undertake some investigation on their own and to develop ideas and apply them. They will also produce a report for each.