This book fills a gap between theory-oriented investigations in PDE-constrained optimization and the practical demands made by numerical solutions of PDE optimization problems. The authors discuss computational techniques representing recent developments that result from a combination of modern techniques for the numerical solution of PDEs and for sophisticated optimization schemes. Computational Optimization of Systems Governed by Partial Differential Equations offers readers a combined treatment of PDE-constrained optimization and uncertainties and an extensive discussion of multigrid optimization. It provides a bridge between continuous optimization and PDE modeling and focuses on the numerical solution of the corresponding problems. Audience: This book is intended for graduate students working in PDE-constrained optimization and students taking a seminar on numerical PDE-constrained optimization. It is also suitable as an introduction for researchers in scientific computing with PDEs who want to work in the field of optimization and for those in optimization who want to consider methodologies from the field of numerical PDEs. It will help researchers in the natural sciences and engineering to formulate and solve optimization problems. Contents: Preface;Chapter 1: Introduction; Chapter 2: Optimality Conditions; Chapter 3: Discretization of Optimality Systems; Chapter 4: Single-grid Optimization; Chapter 5: Multigrid Methods; Chapter 6: PDE Optimization with Uncertainty; Chapter 7: Applications; Bibliography; Index.