Molecular magnetism is a new field of research dealing with the synthesis and study of the physical properties of molecular assemblies involving open-shell units. It is essentially interdisciplinary, joining together organic, organometallic and inorganic chemists, as well as theoreticians, physicists and materials scientists.At the core of research into molecular magnetism lie design and synthesis of new molecular assemblies exhibiting bulk properties such as long-range magnetic ordering or bistability with an hysteresis effect, which confers a memory effect on the system. In such terms, magnetism may be considered a supramolecular function.The first eight contributions to this volume present the state of the art in organic supramolecular chemistry, emphasising interlocked systems and molecular trees. The following six articles are devoted to molecular materials constructed from organic radicals and transition metal units. Molecular bistability is then focused on, followed by metal-organic and coordination magnetic materials. A new approach to nano-sized particles closes the work.