The main topic of this book is the physics of solids containing transition elements: 3d − Ti, V, Cr, Mn, … 4d − Nb, Ru, … 5d −Ta, Ir, Pt, … These materials show extremely diverse properties. There are among them metals and insulators; some show metal–insulator transitions, sometimes with a jump of conductivity by many orders of magnitude. Many of these materials are magnetic: practically all strong magnets belong to this class (or contain rare earth ions, the physics of which is in many respects similar to that of transition metal compounds). And last but not least, superconductors with the highest critical temperature also belong to this group (high-Tc cuprates, with Tc reaching ∼ 150 K, or the recently disovered iron-based (e.g., FeAs-type) superconductors with critical temperature reaching 50–60 K).

The main factor determining the diversity of behavior of these materials is the fact that their electrons may have two conceptually quite different states: they may be either localized at corresponding ions or delocalized, itinerant, similar to those in simple metals such as Na (and, of course, their state may be something in between). When dealing with localized electrons, we have to use all the notions of atomic physics, and for itinerant electrons the conventional band theory may be a good starting point.