1. History of Magnetism.- 1.1 Physics and Metaphysics.- 1.2 Gilbert and Descartes.- 1.3 Rise of Modern Science.- 1.4 Electrodynamics.- 1.5 The Electron.- 1.6 The Demise of Classical Physics.- 1.7 Quantum Theory.- 1.8 Modern Foundations.- 1.9 Magnetic Bubbles.- 1.10 Ultimate Thin Films.- 1.11 Dilute Magnetic Alloys.- 1.12 New Directions.- 2. Exchange.- 2.1 Exchange Equals Overlap.- 2.2 Hydrogen Molecule.- 2.3 Three Hydrogen Atoms.- 2.4 Nonorthogonality Catastrophe.- 2.5 Method of Löwdin and Carr.- 3. Quantum Theory of Angular Momentum.- 3.1 Kinetic Angular Momentum.- 3.2 Spherical Harmonics.- 3.3 Reason for Integer l and m.- 3.4 Matrices of Angular Momentum.- 3.5 Pauli Spin Matrices.- 3.6 Compounding Angular Momentum.- 3.7 Equations of Motion of Interacting Angular Momenta.- 3.8 Coupled Boson Representation.- 3.9 Rotations.- 3.10 More on Compound Angular Momentum.- 3.11 Other Representations.- 3.12 Spins One-Half.- 3.13 Spins One.- 3.14 Quadratic Forms.- 4. Many-Electron Wavefunctions.- 4.1 Slater Determinants.- 4.2 Antisymmetrization.- 4.3 States of Three Electrons.- 4.4 Eigenfunctions of Total S2 and SZ.- 4.5 Ground State of Two Electrons: A Theorem.- 4.6 Hund's Rules.- 4.7 p3 Configuration.- 4.8 p2 and p4 Configurations.- 4.9 Independent Electrons.- 4.10 Electrons in One Dimension: A Theorem.- 4.11 The Wronskian.- 4.12 Theorem in Three Dimensions.- 4.13 Ordering Theorem Versus Hund's Rule.- 4.14 Second Quantization.- 5. From Magnons to Solitons: Spin Dynamics.- 5.1 Spin Waves as Harmonic Oscillators.- 5.2 One-Magnon Eigenstates in Ferromagnets.- 5.3 Two-Magnon States and Eigenstates in Ferromagnets.- 5.4 Bound States in One Dimension.- 5.5 Bound States in Two and Three Dimensions.- 5.6 One-Magnon Eigenstates in Heitler-London Solid.- 5.7 Nonlinear Spin Wave Theory.- 5.8 Perturbation-Theoretic Correction.- 5.9 Antiferromagnetic Magnons: The One-Dimensional XY Model.- 5.10 Bethe's Solution of One-Dimensional Heisenberg Antiferromagnet.- 5.11 Linearized Antiferromagnetic Magnons.- 5.12 Nonlinearities in Antiferromagnetism.- 5.13 Ferrimagnetism.- 5.14 Effects of Surfaces on Spin Wave Amplitudes.- 5.15 Vortices.- 5.16 Solitons: Introductory Material.- 5.17 Solitary Wave Solution.- 6. Magnetism in Metals.- 6.1 Bloch and Wannier States.- 6.2 Tight-Binding.- 6.3 Weak Magnetic Properties.- 6.4 Exchange in Solids: Construction of a Model Hamiltonian.- 6.5 Perturbation-Theoretic Derivation of Heisenberg Hamiltonian.- 6.6 Heisenberg Hamiltonian in Metals.- 6.7 Ordered Magnetic Metals: Deriving the Ground State.- 6.8 Kondo Effect.- 6.9 Spin Glasses.- 6.10 Magnetism Without Localized Spins: Preliminaries.- 6.11 Low-Density Electron Gas.- 6.12 Quasi-Particles.- 6.13 Nagaoka's Model.- 6.14 Degenerate Bands and Intra-Atomic Exchange Forces..- 6.15 Magnons in Metals.- 6.16 Marginal Magnetism of Impurities.- 6.17 Correlations and Equivalence to s-d Model.- References.