A comprehensive chapter on superfluidity, phase transitions, and topology is also included, along with topological phase transitions in photonic lattices and a chapter on realising and manipulating topological metals and their exotic properties. A number of advanced topics is also introduced: topological acoustics, light nuclei and their connection to topology, glass transition, collective modes, lattice Chern-Simons, emergent granularity and topological mesoscopic superfluidity. A great article on anomalous collective modes in topological matter is also present, together with a chapter dedicated to influences of geometry and topology in nuclei. [Extracted from the article]