Quantum physics has been highly successful for more than 90
years. Nevertheless, a rigorous construction of interacting
quantum field theory is still missing. Moreover, it is still
unclear how to combine quantum physics and general relativity in
a unified physical theory. Attacking these challenging problems
of contemporary physics requires highly advanced mathematical
methods as well as radically new physical concepts.

This book presents different physical ideas and mathematical
approaches in this direction. It contains a carefully selected
cross-section of lectures which took place in autumn 2014 at the
sixth conference ``Quantum Mathematical Physics - A Bridge
between Mathematics and Physics'' in Regensburg, Germany. In the
tradition of the other proceedings covering this series of
conferences, a special feature of this book is the exposition of
a wide variety of approaches, with the intention to facilitate a
comparison.

The book is mainly addressed to mathematicians and physicists who
are interested in fundamental questions of mathematical physics.
It allows the reader to obtain a broad and up-to-date overview of
a fascinating active research area.