The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians‎.‎ Its topics were centred around string theory‎,‎ M‎-theory‎,‎ and quantum gravity on the one hand‎,‎ and K‎-theory‎,‎ elliptic cohomology‎,‎ quantum cohomology and string topology on the other‎.‎ Geometry and quantum physics developed in parallel since the recognition of the central role of non‎-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super‎-symmetry and string theory‎.‎ With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research‎.‎ For the first time Graeme Segal‎'‎s manuscript ‎'‎The definition of Conformal Field Theory‎'‎ is published‎,‎ which has been greatly influential over more than ten years‎.‎ An introduction by the author puts it into the present context‎.‎