This book presents four survey articles on different topics in mathematical analysis that are
closely linked to concepts and applications in physics. Specifically it discusses global
aspects of elliptic PDEs Berezin-Toeplitz quantization the stability of solitary waves and
sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts
at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present
them clearly. Starting from basic notions these course notes take the reader to the point of
current research highlighting new challenges and addressing unsolved problems at the interface
between mathematics and physics. All contributions are of interest to researchers in the
respective fields but they are also accessible to graduate students.
