Contact and Symplectic Topology

Symplectic and contact geometry naturally emerged from themathematical description of classical physics. The discovery of newrigidity phenomena and properties satisfied by these geometricstructures launched a new research field worldwide. The intenseactivity of many European research groups in this field is reflectedby the ESF Research Networking Programme "e;Contact And Symplectic Topology"e; (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.