Contact and Symplectic Topology

Symplectic and contact geometry naturally emerged from the

mathematical description of classical physics. The discovery of new

rigidity phenomena and properties satisfied by these geometric

structures launched a new research field worldwide. The intense

activity of many European research groups in this field is reflected

by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST).  The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.