Emmanuel Trélat is a full professor at Sorbonne Université (Paris) and is the director of Laboratoire Jacques-Louis Lions. He is the Editor in Chief of the journal ESAIM: Control Calc. Var. Optim. and is Associate Editor of several other journals, including IEEE Trans. Automat. Control and SIAM Review. He has been awarded the SIAM Outstanding Paper Prize (2006), Maurice Audin Prize (2010), Felix Klein Prize (European Math. Society, 2012), Blaise Pascal Prize (french Academy of Science, 2014), Big Prize Madame Victor Noury (french Academy of Science, 2016). He was a sectional speaker at ICM 2018. He is an elected member of Academia Europaea. His research interests range over control theory in finite and infinite dimension, optimal control, stabilization, geometric control, numerical analysis, shape optimization, sub-Riemannian geometry. He has been teaching theoretical and numerical control since 25 years.

• Chapter 1 Controllability.- Chapter 2. Optimal control.- Chapter 3 Stabilization.- Chapter 4 Semigroup theory.- Chapter 5 Linear control systems in Banach spaces.