Preface 1 Introduction 1.1 Magnetism and Other Effects of Electron-Electron Interaction 1.2 Sources of Magnetic Fields 1.3 Getting Acquainted: Magnetite 1.3.1 Charge States 1.3.2 Spin States 1.3.3 Charge Ordering 1.4 Variety of Correlated Systems: An Outline of the Course 2 Atoms, Ions, and Molecules 2.1 Hydrogen Atom in a Magnetic Field 2.1.1 Non-Relativistic Treatment Motion in a Magnetic Field Zeeman Effect (I) 2.1.2 Relativistic Effects Spin-Orbit Coupling Zeeman Effect (II) Problem 2.1 2.2 Direct Exchange Problem 2.2 . Many-Electron Ions Problem . ..1 Coupling to the Magnetic Field Digression: The Bohr-Van Leeuwen Theorem ..2 Hund's Rules Problem 2.4 2.4 Paramagnetism and Diamagnetism 2.4.1 Paramagnetic Susceptibility Magnetization Curve Problems 2.5-2.8 2.4.2 Diamagnetism Digression: Sursrog Fields 2.5 Hydrogen Molecule 2.5.1 Direct Exchange in Non-Orthogonal Orbitals 2.5.2 Kinetic Exchange 2.5.3 Molecular Orbitals versus Heitler-London Solutions to the Problems 3 Crystal Field Theory 3.1 Incomplete Shells in an Anisotropic Environment: CrystaIFields 3.2 The Role of Symmetry Arguments in ntum Mechanics 3.2.1 Irreducible Representations 3.3 The Octahedral Group Problems 3.1-3.2 3.4 Symmetry Properties of Atomic States 3.5 Splitting of a d-Level in Cubic Field 3.5.1 enching the Orbital Angular Momentum 3.5.2 Partial Restoration ofOrbitalMomentum by Spin Orbit Coupling Problems 3.3-3.4 3.5.3 High-Spin versus Low-Spin States 3.6 Jahn-Teller Effect 3.7 Time Reversallnvariance 3.8 The f2 Configuration 3.8.1 Cubic Crystal Field 3.8.2 Tetragonal Crystal Field 3.8.3 Metamagnetic Transition 3.8.4 Exchange Induced Magnetism Problems 3.5-3.6 3.9 DoubleGroups …… 4 Mott Transition and Hubbard Model 5 Mott Insulators 6 Heisenberg Magnets 7 Itinerant Electron Magnetism 8 Ferromagnetism in Hubbard Models 9 The Gutzwiller Variational Method 10 The Correlated Metallic State 11 Mixed Valence and Heavy Fermions 12 ntum Hall Effect A Hydrogen Atom B Sing-S-Flip Ansatz C Gutzwiller Approximation D Schrieffer-Wolff Transformation Bibliography Index