The aim of the first module is to deepen the knowledge and skills especially in the modern theory of dynamical systems and give the student a solid appreciation of the deep connections between mathematics and other scientific disciplines, both in terms of the mathematical problems that they inspire and the important role that mathematics plays in scientific research and industry. Mathematical software tools, and others, will be used to implement algorithms for the solution of the real world problems studied during the course. At the end of the course the student is expected to be able to complete professional and technical tasks of a high level in the context of mathematical modelling and computation, both working alone and in groups. In particular the student will be able to write a model of a real problem, to recognise the effective parameters and analyse the model and its possible implications. The second module wants to provide sufficient theoretical and numerical background for the optimal control of dynamical systems. Such problems will be developed by means of real application examples, and recent research studies. At the end of the course students will be able to decide which numerical method is suitable for the solution of some specific optimal control problems. He/She will be able to provide theoretical results on the controllability and stability of certain optimal control problem and numerical methods. He/She will be able to develop his/her own code, and capable choose the appropriate optimization method for each application shown during the course.