Max Born Symposia started in 1991, as the continuation of series of Leipzig-Wroclaw semiars in theoretical physics that were held in 1970’s and 1980’s. Since 1991 already 32 Symposia have been organized, reviewing different frontline research domains of theoretical physics.

XXXIII-th Max Born Symposium is devoted to the recent developments in the research fields of noncommutative geometry and quantum symmetries, with the emphasis on their links with quantum gravity. We recall that in the past frequently it has been argued that the classical space-time and standard relativistic symmetries should not be applied at very short, Planckian distances. The aim of the Symposium is to contribute to future mathematical framework of quantum gravity, the theoretical concept which is at present the main challenge faced by present theory of fundamental interactions. Although the original plan was to publish the Proceedings in the printed form, as conference volume, in order to include all important contributions to the meeting we have decided to provide the conference content in the internet form. The proceedings lacks therefore a uniform formal rule, and the files reflect various personal ways of delivering the lectures.

The Symposium was organized jointly by Institute for Theoretical Physics of Wroclaw University and Polish Academy of Science, with the financial support also of Polish National Center of Science. The members of the Organizing Committee (A.Borowiec, A.Frydryszak, J.Kowalski-Glikman, J.Lukierski, A. Pachol, M. Trzesniewski) carried all burdens of the preparation of the meeting.