Andrea Manzoni, PhD, is an Associate Professor of Numerical Analysis at Politecnico of Milan. He is the author of 2 books and of approximately 50 papers. In 2012 he won the ECCOMAS Award for the best PhD thesis in Europe about Computational Methods in Applied Sciences and Engineering and the Biannual SIMAI prize (Italian Society of Applied and Industrial Mathematics) in 2017. His research interests include the development of reduced-order modelling techniques for PDEs, PDE-constrained optimization, uncertainty quantification, computational statistics, and machine/deep learning.

Alfio Quarteroni is a Professor of Numerical Analysis at Politecnico of Milan and Professor Emeritus at EPFL, Lausanne. He is the author of 25 books, editor of 12 books, author of about 400 papers. He is the recipient of two ERC Advanced Grants. He is a member of the Italian Academy of Science, the European Academy of Science, Academia Europaea, and the Lisbon Academy of Science. His research Group at EPFL has carried out the mathematical simulation for the Alinghi sailing boat, the winner of two editions (2003 and 2007) of America's Cup. His research interests include mathematical modeling and its applications at large.

Sandro Salsa is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on free boundary problems. He is an author of 13 books and several papers in the most prestigious scientific mathematical journals.

1 Introduction: Representative Examples, Mathematical Structure.- Part I A Preview on Optimization and Control in Finite Dimensions.- 2 Prelude on Optimization: Finite Dimension Spaces.- 3 Algorithms for Numerical Optimization.- 4 Prelude on Control: The Case of Algebraic and ODE Systems.- Part II Linear-Quadratic Optimal Control Problems.- 5 Quadratic control problems governed by linear elliptic PDEs.- 6 Numerical Approximation of Linear-Quadratic OCPs.- 7 Quadratic Control Problems Governed by Linear Evolution PDEs.- 8 Numerical Approximation of Quadratic OCPs Governed by Linear Evolution PDEs.- Part III More general PDE-constrained optimization problems.- 9 A Mathematical Framework for Nonlinear OCPs.- 10 Advanced Selected Applications.- 11 Shape Optimization Problems.- Appendix A Toolbox of Functional Analysis.- Appendix B Toolbox of Numerical Analysis.