Nanomagnetism is a rapidly expanding area of research in nanoscience, opening perspectives of novel applications. Magnetic molecules are at the very bottom of the possible size of nanomagnets, and they provide a unique opportunity to observe the coexistence of quantum and classical properties. The discovery in the early 1990s that a cluster comprising twelve manganese ions shows magnetic hysteresis of molecular origin accompanied by quantum tunnelling of the magnetization opened a new research, which is flourishing through the collaboration of chemists and physicists. The field is often indicated as single molecule magnets (SMM). This book attempts to cover in detail the area of molecular nanomagnetism — a branch of molecular magnetism — using a language which should be understood by both the physical and chemical communities. The book starts from the development of theory needed to understand the nature of the properties of molecular nanomagnets, including magnetic coupling and magnetic anisotropy. The most common experimental techniques needed to investigate the properties of molecular nanomagnets are covered to allow the reader to understand how sophisticated instrumentation can provide unique information on SMM. Particular attention is devoted to magnetic relaxation, highlighting the interplay of classical and quantum behaviours. Appendices cover topics which would require too many digressions in the main text, ranging from systems of units to master equations for the density matrix.