from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on ¿Constrained Optimization, Identification and Control¿, ¿Shape and Topology Optimization¿, ¿Adaptivity and Model Reduction¿, ¿Discretization: Concepts and Analysis¿ and ¿Applications¿. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.