Written for beginning graduate and advanced undergraduate students, the textbook introduces concepts such as topological systems, Weyl and Majorana symmetries in solids, Berry’s phase and coherent boundary conditions, Wilczek time crystals, anyons, and Dirac fermions. With that, the book closes the gap between traditional solid state physics textbooks and more technology- and device-oriented overviews for advanced professionals. By using basic, well-established solid-state models coupled with intuitive physical reasoning and detailed and annotated mathematical appendices, the textbook enables its readers to connect their knowledge from introductory quantum mechanics and solid-state physics courses with the advanced concepts put forward in courses on quantum materials.