This volume presents state-of-the-art research in mathematical physics addressed to a broad spectrum of readers, including graduate students, researchers, and others interested in this topic. Contributors to the volume participated in the 13th International Congress on Mathematical Physics held at Imperial College (London, UK). The contributions include, in particular, pedagogical lectures presented at the Young Researchers Symposium (YRS) held in association with the Congress, as well as public lectures given at the Congress, and the contributions from the winners of the Henri Poincare prize.