1 Introduction. - 1. 1 Electronic Structure of Solids. - 1. 2 Systems with Reduced Symmetry. - 1. 3 Tight-Binding Approximation. - 1. 4 Resolvents and Green Functions. - References. - 2 Linear Muffin-Tin Orbital (LMTO) Method. - 2. 1 Secular Equation. - 2. 2 Variational Principle. - References. - 3 Green Function Method. - 3. 1 Green Functions in Solids. - 3. 2 Tight-Binding LMTO Method. - 3. 3 Relation to the KKR Method. - 3. 4 Green Functions in Layered Systems. - 3. 5 Calculation of Observables. - References. - 4 Coherent Potential Approximation (CPA). - 4. 1 Configurational Average of Green Function. - 4. 2 Single-Site Approximation. - 4. 3 Calculation of Observables. - 4. 4 Properties and Limitations of the CPA. - References. - 5 Selfconsistency Within Atomic Sphere Approximation. - 5. 1 Charge Selfconsistency. - 5. 2 Electrostatic (Madelung) Fields. - 5. 3 Total Energy. - References. - 6 Relativistic Theory. - 6. 1 Relativistic TB-LMTO Method: Non-Magnetic Case. - 6. 2 Relativistic TB-LMTO Method: Spin-Polarized Case. - References. - 7 Bulk Systems Overlayers and Surfaces. - 7. 1 Bulk Elemental Metals. - 7. 2 Bulk Transition-Metal Alloys. - 7. 3 Clean Surfaces and Overlayers. - 7. 4 Random Overlayers. - 7. 5 Surfaces of Random Alloys. - References. - 8 Magnetic Properties. - 8. 1 Ferromagnetic Bulk Alloys. - 8. 2 Magnetism of Surfaces and Interfaces. - 8. 3 Disordered Local Moments. - References. - 9 Effective Interatomic Interactions in Alloys. - 9. 1 Ising Model for Alloys. - 9. 2 Generalized Perturbation Method. - 9. 3 Bulk Systems. - 9. 4 Surfaces. - 9. 5 Concluding Remarks. - References. - 10 Numerical Implementation. - 10. 1 Tight-Binding Structure Constants. - 10. 2 Radial Schrödinger and Dirac Equations. - 10. 3 Complex Contour Energy Integration. - 10. 4 Analytic Continuation. - 10. 5 Brillouin Zone Integration. - 10. 6 Surface Green Functions. -10. 7 Coherent Potential Approximation. - 10. 8 Local Spin Density Approximation. - References. Language: English