The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantization of geometrical objects. The majority of lectures at the Advanced Study Institute on Quantum Ge- ometry in Akureyri was on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary par- ticles and interactions. The geometric concept of one-dimensional extended objects, or strings, has always been at the core of superstring theory but...

The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantization of geometrical objects. The majority of lectures at the Advanced Study Institute on Quantum Ge- ometry in Akureyri was on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary par- ticles and interactions. The geometric concept of one-dimensional extended objects, or strings, has always been at the core of superstring theory but...