This text discusses the qualitative properties of dynamical systems including both differential equations and maps, The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams to develop the material including a treatment of chaotic behaviour. The unprecedented popular interest shown in recent years in the chaotic behaviour of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. The book is aimed at courses in dynamics, dynamical systems and differential equations and dynamical systems for advanced undergraduates and graduate students. Applications in physics, engineering and biology are considered and introduction to fractal imaging and cellular automata are given.