This accessible new text introduces the theoretical concepts and tools essential for graduate-level courses on the physics of materials in condensed matter physics, physical chemistry, materials science and engineering, and chemical engineering. Topics covered range from fundamentals such as crystal periodicity and symmetry, and derivation of single-particle equations, to modern additions including graphene, two-dimensional solids, carbon nanotubes, topological states, and Hall physics. Advanced topics such as phonon interactions with phonons, photons and electrons, and magnetism, are presented in an accessible way, and a set of appendices reviewing crucial fundamental physics and mathematical tools makes this text suitable for students from a range of backgrounds. Students will benefit from the emphasis on translating theory into practice, with worked examples explaining experimental observations, applications illustrating how theoretical concepts can be applied to real research problems, and 242 informative full color illustrations. End-of chapter exercises are included for homework and self-study, with solutions and lecture slides for instructors available online.