Quantum magnetism is one of the thriving branches of condensed matter physics, and it has been so for a few decades. Magnetism of materials is important not only for practical applications, but because certain magnetic compounds host exotic fundamental physics that can be studied experimentally. Materials magnetism is an entirely quantum phenomenon and emerges from the collective behaviour of electrons in the solid, rather than from their individual properties as elementary particles. This textbook offers a concise overview of the most important concepts in quantum magnetism, while also positioning the subject within the broader science of magnetism. Fortunately, magnetism is one of those areas of physics where insightful experimental data can be obtained by multiple techniques and quantitatively compared to theory. The book opens with a systematic discussion of linear response theory in the context of magnetic matter. Everything else, such as the magnetism of the electron gas, of individual ions, and of strongly interacting systems, is viewed through the lens of linear response. This approach allows us to move from simple to more complex, quantum systems, while remaining within the same framework. All the derivations are rigorous but explained in accessible terms.Advanced students in theory and experiment will gain a thorough understanding of the theoretical foundation of magnetism, coupled with numerous modern and classic experimental examples.