In recent years the foundations of quantum theory have seen a boost of interest and development. This is on the one hand due to their crucial role in new developments such as quantum information theory, quantum computing, and nano-scale physics. On the other hand, it is due to the increasing recognition of their relevance in big unsolved questions such as quantum gravity and black hole physics. At the same time, successful theories of physics have always relied on and driven mathematical development. The fruitful interaction with physics extends to almost all areas of mathematics, but is arguably most broad and intense at the foundations of physics.